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Full text of "Design of wood aircraft structures"

The contents uf t h 1 > 
ia part without tpei 



letin shall not M 
authorization of 



the Aeronautical Board* 



ANC— 18 
June, 1944 



ANC BULLETIN 



DESIGN OF WOOD 
AIRCRAFT STRUCTURES 

WAR DEPARTMENT 
ARMY AIR FORCES 

NAVY DEPARTMENT 
BUREAU OF AERONAUTICS 

DEPARTMENT OF COMMERCE 
CIVIL AERONAUTICS ADMINISTRATION 



Issued by the 

ARMY-NAVY-CIVIL COMMITTEE 
» on 
AIRCRAFT DESIGN CRITERIA 

Under the supervision of the 
AERONAUTICAL BOARD 

The contents of this bulletin shall not be reproduced in whole or 
in part without specific authorization of the Aeronautical Board. 



UNITED STATES GOVERNMENT PRINTING OFFICE 
WASHINGTON: 1944 



This Bulletin 
by 

FOREST PRODUCTS LABORATORY 
FOREST SERVICE 
UNITED STATES DEPARTMENT OF AGRICULTURE 

and 

ARMY-NAVY-CIVIL COMMITTEE 
on 

AIRCRAFT DESIGN CRITERIA 



I] 



NOTICE 

The reader is hereby notified that this bulletin is subject to revision and amend- 
ment when and where such revision or amendment is necessary to effect 
agreement with the latest approved information on aircraft design criteria. 
When using this bulletin, the reader should therefore make certain that it is 
the latest revision and that all issued amendments, if any, are known. 



Ill 



TABLE OF CONTENTS 



Page 



CHAPTER 1. GENERAL 1 

1.0. Purpose and Use of Bulletin 1 

1.1. Nomenclature , 1 

CHAPTER 2. STRENGTH OF WOOD AND PLYWOOD ELEMENTS 9 

2.0. Physical Characteristics of Wood 13 

2.1. Basic Strength and Elastic Properties of Wood- . . , 16 

2.2. Columns 28 

2.3. Beams 30 

2.4. Torsion 36 

2.5. Basic Strength and Elastic Properties of Plywood 37 

2.6. Plywood Structural Elements 59 

2.7. Flat Rectangular Plywood Panels 76 

2.8. Curved Plywood Panels 109 

2.9. Joints 114 

CHAPTER 3. METHODS OF STRUCTURAL ANALYSIS 131 

3.0. General 133 

3.1. Wings 135 

3.2. Fixed Tail Surfaces 185 

3.3. Movable Control Surfaces 185 

3.4. Fuselages 185 

3.5. Hulls and Floats • 199 

3.6. Miscellaneous 201 

CHAPTER 4. DETAIL STRUCTURAL DESIGN 204 

4.0. General 205 

4.1. Plywood Covering 205 

4.2. Beams 210 

4.3. Ribs 216 

4.4. Frames and Bulkheads 220 

4.5. Stiffeners 220 

4.6. Glue Joints 222 

4.7. Mechanical Joints 224 

4.8. Miscellaneous Design Details 227 

4.9. Examples of Actual Design Details 233 



IV 



CHAPTER 1. GENERAL 



1.0. PURPOSE AND USE OF BULLETIN. 

1.00. Introduction. This bulletin has been prepared for use in the design of both 
military and commercial aircraft, and contains material which is acceptable to the Army 
Air Forces, Navy Bureau of Aeronautics, and the Civil Aeronautics Administration. 
It should, of course, be understood that methods and procedures other than those out- 
lined herein are also acceptable, provided they are properly substantiated and approved 
by the appropriate agency. The applicability and interpretation of the provisions of 
this bulletin as contract or certification requirements will in each case be defined 
by the procuring or certificating agency. 

1.01. Scope of Bulletin. The technical material in this bulletin is contained in 
chapters 2, 3, and 4, and pertains to three related phases of the structural design of 
wood aircraft. 

Chapter 2 presents information on the strength and elastic properties of structural 
elements constructed of wood and plywood. This information supersedes that contained 
in the October 1940 edition of ANC-5, "Strength of Aircraft Elements." 

Those sections of chapter 2, which are based on incomplete data or theoretical 
analysis, that have not been fully verified by test have been, as a caution, marked with 
a double asterisk. Those sections that are based on reasonably complete information 
but require further substantiating tests are marked with a single asterisk. The use of 
the various formulas and data in these sections should, therefore, be commensurate 
with the limitations noted. Since further research on the strength and elastic properties 
of wood and plywood structural elements is being actively carried on by the Forest 
Products Laboratory, it is anticipated that revisions to chapter 2 will be made from 
time to time as this work progresses. 

Chapter 3 contains suggested methods of structural analysis for the design of various 
aircraft components. Although these methods are in many cases the same as those 
used for metal structures, special considerations have been introduced which take into 
account the orthotropic properties of wood. 

Chapter 4 presents recommendations on the detail structural design of wood air- 
craft and contains some examples of how various manufacturers have treated the solu- 
tion of specific detail design problems. 

1.02. Acknowledgement. The ANC Committee on Aircraft Design Criteria and 
the Forest Products Laboratory express their appreciation to aircraft manufacturers 
and others for the valuable assistance given in connection with various parts of this 
bulletin. 

1.1. NOMENCLATURE.This section presents the definitions of standard structural 
symbols which are used in the bulletin. In addition, sections 1.10 and 1.11 are presented 
to clarify the differentiation between the definitions for strength and elastic properties 
of plywood elements and those for like properties of plywood panels. These sections 
also outline the use of table 2-9. 



1 



2 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



1.10. Definitions for Plywood Elements — Beams, Prisms and Columns in Com- 
pression, Strips in Tension. A plywood element is any rectangular piece of plywood 
that is supported, loaded, or restrained on two opposite edges only. In defining the 
various strength and elastic property terms for plywood elements; the face grain direc- 
tion has been used as a reference; for example, the subscript w denotes a direction 
parallel to (with) the face grain, while the subscript x denotes a direction perpendicular 
to (across) the face grain. This is illustrated by figure 1-1. The strength and elastic 
properties given in table 2-9 of the bulletin are for plywood elements. 



Figure 1-1. — Plywood element (supported, loaded, or restrained on two opposite edges only). 

1.11. Definitions for Plywood Panels 1 . A plywood panel is any rectangular piece 
of plywood that is supported, loaded, or restrained on more than two edges. In defining 
the various strength and related property terms for plywood panels, the side of length a 
rather than the face grain direction has been used as the reference. For any panel having 
tension or compression loads (either alone or accompanied by shear) the side of length a 
is the loaded side. For panels having only shear loads (with no tension or compression), 
the side a may be taken as either side. (Sec. 2.701). For panels having normal loads, 
side a is the shorter side. The subscripts a and 1 denote a direction parallel to the side 
of length a, and the subscripts b and 2 denote a direction perpendicular to the side of 
length a. This is illustrated by figure 1-2. Since, in panels, the directions in which 
E a , E b , Ei, E 2 , etc., are to be measured are related to the directions of the sides of lengths 
a and b, it is necessary to relate these directions to the face grain direction before the 
terms can be evaluated from table 2-9. It may be stated, therefore, that: 




TABLE Z-3 



TABLE 2-9 



b 



E a . E f , ETC— CANNOT BE L E i) ,E 2 , ETC— CANNOT BE 
EVALUATED UNTIL EACE EVALUATED UNTIL FACE 
GRAIN DIRECTION 15 KNOWN GRAIN DIRECTION 15 If NO INN 




Figure 1-2. — Plywood panel (supported, loaded, or restrained on more than two edges). 



1 The designations for sides a and b as used herein are different from those used in ANC-5, in which 
the side of length h is defined as the loaded side in tension or compression and as the short side in shear 



GENERAL 



3 



( 1 ) When the face grain direction of a plywood panel is parallel to the side of length 
a, the values of E a , E h , E h E>, etc, may be taken from the columns for E w , E T , E fw , E fx , 
etc., respectively, in table 2 9. This is illustrated by figure 1-3. 




E^.E,, ETC.- VALUES FROM 
COLUMNS FOR E Wt E fw ,ETC. 



E^ ETC.- VALUES FROM 



COLUMNS FOR E Xt E fx ,ETC. } 
RES PEC TI VEL Y t IN TABLE RE5PECTIVEL Y, IN TABLE 
Z-9 2-9 

Figure 1-3. — Plywood panel (face grain direction parallel to side of length a). 



(2) When the face grain direction of a plywood panel is perpendicular to the side 
of length a, the values of E a , E b , E,, Eg, etc., may be taken from the' columns for E x , 
E w , E fx , E fw , etc., respectively, in table 2-9. This is illustrated by figure 1-4. 



T 

a 

1 



////////////////// ////////// 



FACE GRAIN 
' DIRECTION 



V77777777, 



E„ E ETC-VALUES FROM 



7Z 



E b ,E z> ETC -VALUES FROM 



COL UMAI5 FOR E x , E fx , ETC, COL UMNS E„ t E fw ,ETC, 

RESPECTIVELY, IN TABLE RESPECTIVELY, 7n TABLE 
2.-3 2-9 

Figure 1-4. — Plywood panel (face grain direction perpendicular to side of length a). 

1.12. STANDARD STRUCTURAL SYMBOLS FOR CHAPTER TWO. In 

general, symbols that are used only in the section where they are defined are not included 
in this nomenclature. » 



-area of cross section, square inches 
(total). 



-area of plies with grain direction parallel 
to the direction of applied stress. 



-The length of the loaded side of a ply- 
wood panel for compression or tension 
loads, and the length of either side for 
shear loads (Sec. 2.701); subscript de- 
noting parallel to side of length a for 
plywood panels. 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



-area of plies with grain direction per- 
pendicular to the direction of applied 
stress (surfaces of plies parallel to plane 
of glue joint tangential to the annual 
growth rings, as for rotary-cut or flat- 
sliced veneer, flat-sawn lumber). 

-area of plies with grain direction per- 
pendicular to the direction of applied 
stress (surfaces of plies parallel to plane 
of glue joint radial to the annual growth 
rings, as for quarter-sliced veneer, 
quarter-sawn lumber). 



circumference 



-diameter 

-modulus of elasticity of wood in the 
direction parallel to the grain, as de- 
termined from a static, bending test. 
(This value is listed in table 2-4.) 

-modulus of elasticity of wood in the 
direction radial to the annual growth 
rings. 

modulus of elasticity of wood in the 
direction tangential to the annual growth 
rings. 

modulus of elasticity of wood in the 
direction parallel to the grain, as de- 
termined from a compression test 
(value not listed in table 2-4, but ap- 
proximately equal to 1.1 El). 



-effective modulus of elasticity of ply- 
wood in tension or compression measured 
parallel to the side of length a of ply- 
wood panels. 



b — the length of the unloaded side of a ply- 
wood panel for compression or tension 
loads, and the length of either side for 
shear loads (Sec. 2.701); subscript de- 
noting parallel to side of length b for 
plywood panels; subscript denoting 
"bending" for solid wood. 

br — subscript denoting "bearing." 

c — end-fixity coefficient for columns; sub- 
script denoting "compression '; distance 
from neutral axis to extreme fiber. 

c' — distance fr om neutral axis to the extreme 
fiber having grain direction parallel to 
the applied stress (plywood). 

cr — subscript denoting "critical." 

d —depth or height 

cz, — unit strain (tension or compression) in 
the L direction. 



cr — unit strain (tension or compression) in 
the R direction. 

ct — unit strain (tension or compression) in 
the T direction. 



(Lit 



-unit strain (shear) or the change in 

angle between lines originally drawn in 

the L and T directions, 
-unit strain (shear) or the change in 

angle between lines originally drawn in 

t he L and R directions, 
-unit strain (shear) or the change in 

angle between lines originally drawn in 

the T and R directions. 



GENERAL 



5 



Eb — effective modulus of elasticity of ply- 
wood in tension or compression measured 
perpendicular to the side of length a of 
plywood panels. 

E w — effective modulus of elasticity of ply- 
wood in tension or compression measured 
parallel to (with) the grain direction of 
the face plies. 

E x — effective modulus of elasticity of ply- 
wood in tension or compression measured 
perpendicular to (across) the grain <li- 
rection of the face plies. 

Ef W — effective modulus of elasticity of ply- 
wood in flexure (bending) measured 
parallel to (with) the grain direction of 
the face plies. 

E fx — effective modulus of elasticity of ply- 
wood in flexure (bending) measured per- 
pendicular to (across) the grain direction 
of the face plies. 

E' f X — same as Ef X , except that outermost ply 
on tension side is neglected (not to he 
used in deflection formulas). 

E\ — effective modulus of elasticity of ply- 
wood in flexure (bending) measured 
parallel to the side of length a of ply- 
wood panels. 

E-i — effective modulus of elasticity of ply- 
wood in flexure (bending) measured per- 
pendicular to the side of length a of 
plywood panels. 

F — allowable stress; stress determined from 
test. 

Fb — allowable bending stress. 



/''(,„ — modulus of rupture in bending for solid 
wood parallel to grain. 

Fb P — fiber stress at proportional limit in bend- 
ing for solid wood parallel to grain. 

Fbrp — bearing stress at proportional limit 
parallel to the grain for solid wood. 

Fbrr — allowable ultimate bearing stress per- 
pendicular to grain for solid wood (either 
radial or tangential to the annual growth 
rings). 

Fbru — allowable ultimate bearing stress parallel 
to grain. 



/ — internal (or calculated) stress; subscript 
denoting "flexure" (bending) for ply- 
wood. 

fb — internal (or calculated) primary bend- 
ing stress. 



fbr — internal (or calculated) bearing stress 



i 

6 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



— allowable compressive stress. 

— critical compressive stress for the 
buckling of rectangular plywood panels. 



/„ — internal (or calculated) compressive 
stress. 

jcL — internal (or calculated) compressive 
stress in a longitudinal ply; i.e., any 
ply with its grain direction parallel to 
the applied stress. 



F C p — stress at proportional limit in compres- 
sion parallel to grain for solid wood. 

F cp T — stress at proportional limit in com- 
pression perpendicular to grain for solid 
wood (either radial or tangential to the 
annual growth rings). 

Fcpw — stress at proportional limit in compres- 
sion for plywood having the face grain 
direction parallel to {with) the applied 
stress. 

F CP x — stress at proportional limit in com- 
pression for plywood having the face 
grain direction perpendicular to (across) 
the applied stress. 

F,,,e — stress at proportional limit in com- 
pression for plywood having the face 
grain direction at an angle 6 to the 
applied stress. 

F cu —ultimate compressive stress parallel to \ 

the grain for solid wood. 
F cuT — compressive strength perpendicular to 

grain for solid wood (either radial or 

tangential to the annual growth rings). 

Taken as 1 .33 times F cp t- 
Fcnw — ultimate compressive stress for ply- 
wood having the face grain direction 

parallel to (with) the applied stress. 
F ruI — ultimate compressive stress for plywood 

having the face grain direction perpen- 
dicular to (across) the applied stress. 
FcuO — ultimate compressive stress for plywood 

having the face grain direction at an 

angle 6 to the applied stress. 
F s — allowable shearing stress. V — internal (or calculated) shearing stress. 

F Scr — critical shear stress for the buckling of 

rectangular plywood panels. 
F st — modulus of rupture in torsion. 
F S u — ultimate shear stress parallel to grain 

for solid wood. 
F s d c — untimate shear stress for plywood, 

wherein 6 designates the angle between 

the face grain direction and the shear 

stress in a plywood element so loaded in 

shear that the face grain is stressed in 

compression. 



c 



GENERAL 



7 



F s 8t — ultimate shear stress for plywood, 
wherein 6 designates the angle between 
the face grain direction and the shear 
stress in a plywood element so loaded 
in shear that the face grain is stressed 
in tension. 

F swx — ultimate shear stress for plywood ele- 
ments for the case where the face grain 
is at 0° and 90° to the shear stress. 

Ft —allowable tension stress. 



ft — internal (or calculated) tensile stress. 

f t L — internal (or calculated) tensile stress in 
a longitudinal ply (any ply with its 
grain direction parallel to the applied 
stress). 



Ftu — ultimate tensile stress parallel to grain 
for solid wood. 

F tU T — tensile strength perpendicular to grain 
for solid wood (either radial or tan- 
gential to the annual growth rings). 

F lU w — ultimate tensile stress for plywood hav- 
ing the face grain direction parallel to 
(with) the applied stress. 

F tux — ultimate tensile stress for plywood 
having the face grain direction perpen- 
dicular to (across) the applied stress. 

FtuB — ultimate tensile stress for plywood hav- 
ing the face grain direction at an angle 
6 to the applied stress. 

G — mean modulus of rigidity taken as 1/16 
of E L . 

Gl,t — modulus of rigidity associated with shear 
deformations in the LT plane resulting 
from shear stresses in the LR and RT 
planes. 

Glr — modulus of rigidity associated with shear 
deformations in the LR plane resulting 
from shear stresses in the LT and RT 
planes. 

Gj r — modulus ot rigidity associated with shear 
deformations in the TR plane resulting 
from shear stresses in the LT and LR 
planes. 

H — 

I — moment of inertia. 
1 P — polar moment of inertia. 
,/ — Torsion constant (I p for round tubes). 
A" — a constant, generally empirical. 
L — length; span; subscript denoting the 
direction parallel to the grain. 
L 

L' = —where c is the end fixity coefficient. 
V c 

M — applied bending moment. 

N — 



h — height or depth. 

i — subscript denoting "ith ply." 



j — stiffness factor \/EI/P 
k — 

I — not used, to avoid confusion with the 
numeral 1. 



in — 

n — number of plies. 



8 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



P — applied load (total, not unit load). 



(J — static moment of a cross section. 

R — subscript denoting the direction radial 
to the annual growth rings and per- 
pendicular to the grain direction. 

S — shear force. 

T — applied torsional moment, torque; sub- 
script denoting the direction tangential 
to the annual growth rings and per- 
pendicular to the grain direction. 

U 

w — 



Z — section modulus, I/c 

Z,, — polar section modulus, I p /c. 

* — a single asterisk after a section number 
indicates that the section is based on 
resonably complete information but re- 
quires further substantiating tests. 

** — double asterisks indicate sections, based 
on incomplete data or theoretical an- 
alysis, that have not been fully verified 
by test. 



l> — subscript denoting "polar"; subscript 
denoting "proportional limit"; load per 
unit area. 

psi — pounds per square inch. 

q — shear flow, pounds per inch. 

r —radius. 



s — subscript denoting "shear." 

t — thickness; subscript denoting "tension." 



i, — thickness of central ply. 

tj — thickness of face ply. 

u — subscript denoting "ultimate." 

w — deflection of plywood panels; load per 

linear inch; subscript denoting parallel 

to face grain ot plywood. 
x subscript denoting perpendicular to face 

grain of plywood. 
?/ — distance from the neutral axis to any 

given fiber. 

2 

(i — the angle between side of length b and 
the face grain direction as used in 
the determination of buckling criteria 
for panels (Sec. 2.70). 

— deflection. 

— usually the acute angle in degrees be- 
tween the face grain direction and the 
direction of the applied stress; angle 
of twist in radians in a length (L). 

Illt — Poisson's ratio of contraction along the 
direction T to extension along the 
direction L due to a normal tensile 
stress on the RT plane; similarly, [llrj 

V-KT, V-TR, V-IiL, and \kTL- 

p — radius of gyration. 

4> — usually the acute angle in degrees be- 
tween the face grain direction and the 
axis of extension. 



CHAPTER 2. STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



TABLE OF CONTENTS 



2.0. PHYSICAL CHARACTERISTICS 

OF WOOD 13 

2.00. Anisotropy of Wood 13 

2.01. Density or Apparent Specific 

Gravity 15 

2.02. Moisture Content 15 

2.03. Shrinkage Hi 

2.1. BASIC STRENGTH AND ELAS- 

TIC PROPERTIES OF 
WOOD 16 

2.10. Design Values, Table 2-3 16 

2.100. Supplemental Notes 21 

2.1000. Compression Perpendicular to 

Grain 21 

2.1001. Compression Parallel to Grain . 21 

2.11. Notes on the Use of Values 

in Table 2-3 21 

*2.110. Relation of Design Values in 

Table 2-3 to Slope of Grain . . 21 

2.111. Tension Parallel to Grain 21 

2.112. Tension Perpendicular to 

Grain 22 

2.12. Standard Test Procedures. 22 

2.120. Static Bending 22 

2.1200. Modulus of Elasticity (E L ) ... 22 

2.1201. Fiber Stress at Proportional 

Limit (F bp ) 24 

2.1202. Modulus of Rupture (F bll ) 24 

2.1203. Work to Maximum Load 24 

2.121. Compression Parallel to Grain . 24 

2.1210. Modulus of Elasticity (E Lc ) ... . 24 

2.1211. Fiber Stress at Proportional 

Limit (F cp ) 25 

2.1212. Maximum Crushing Strength 

(F cu ) 25 

2.122. Compression Perpendicular to 

Grain 25 

2.123. Shear Parallel to Grain (F sv ) ... 25 

2.124. Hardness 27 

2.125. Tension Perpendicular to 

Grain (F tuT ) 27 

2.13. Elastic Properties Not In- 

cluded in Table 2-3 27 

2.130. Moduli of Elasticity Perpen- 
dicular to Grain (E T , Er). . . . 27 

•2.131. Moduli of Rigidity (Glt, Glr, 

G bt ) 27 

*2.132. Poisson's Ratios ([/.) 28 

2.14. Stress-Strain Relations 28 



2.2. COLUMNS 28 

2.20. Primary Failure 28 

2.21. Local Buckling and Twisting 

Failure 28 

2.22. Lateral Buckling 23 

2.3. BEAMS 30 

2.30. Form Factors 30 

2.31. Torsional Instability 32 

2.32. Combined Loadings 32 

2.320. General 32 

2.321. Bending and Compression 32 

2.322. Bending and Tension 34 

2.33. Shear Webs 34 

2.34. Beam Section Efficiency 34 

2.4. TORSION 36 

2.40. General 36 

2.41. Torsional Properties 36 

2.5. BASIC STRENGTH AND ELASTIC 

PROPERTIES OF PLY- 
WOOD 37 

2.50. General 37 

2.51. Analysis of Plywood Strength 

Properties (General) 38 

2.52. Basic Formulas 39 

*2.53. Approximate Methods for 

Calculating Plywood 

Strengths 42 

2.54. Moisture-Strength Relations 

for Plywood 42 

2.540. General " 42 

2.541. Approximate Methods for 

Making Moisture Correc- 
tions for Plywood Strength 

Properties 42 

2.5410. Moisture Corrections for Ply- 
wood Compressive Strength 
(0° or 90° to Face Grain Di- 
rection) 43 



*2.5411. Moisture Corrections for Ply- 
wood Tensile Strength (0° or 
90° to Face Grain Direction). 43 

*2.5412. Moisture Corrections for Ply- 
wood Shear Strength (0° or 
90° to Face Grain Direction). 43 
2.5413. Moisture Corrections for Ply- 
wood Compressive Strength 
(Any Angle to Face Grain 
Direction) 43 



9 



10 



2.5414. Moisture Corrections for Ply- 
wood Tensile Strength (Any 
AngletoFace Grain Direction) . 43 

2.5415. Moisture Corrections for Ply- 

wood Shear Strength (Any 
Angleto Face Grain Direction ) 43 
2.55. Specific Gravity- Strength Re- 



lations for Plywood 43 

2.56. Stress-Strain Relations for 

Wood and Plywood 45 

2.560. Derivation of General Stress- 
Strain Relations for Plywood. . . 46 

2.5600. Obtaining Strains from 

Given Stresses 46 

2.5601. Obtaining Stresses from 

Given Strains 46 

2.561. Stress-Strain Relations for 
Specific Cases 49 

*2.5610. Stress -and Strain -Circle Con- 
stants 49 

2.5611. Stress-Strain Relations in 

45° Plywood 54 

2.56110. Tension at 45° to the Face 
Grain 55 

2.56111. Shear at 45° to the Face 
Grain 57 

*2. 56112. Experimental Stress -Strain 

Data 59 

2.6. PLYWOOD STRUCTURAL ELE- 

MENTS 59 

2.60. Elements (0 =0° or 90°) 59 

2.600. Elements in Compression 

(6=0° or 90°) 59 

*2.601. Elements in Tension 

(8=0° or90°) 61 

*2.602. Elements in Shear 

(8 =9° or 90°).... 61 

2.61. Elements (8 = Any Angle) 61 

*2.610. Elements in Compression 

(6 = Any Angle) 61 

2.61 1 . Elements in Tension 

(8 = Any Angle) 62 

*2.612. Elements in Shear 

(8 = Any Angle) 62 

*2.613. Elements in Combined Com- 
pression (or Tension) and 

Shear (6 = Any Angle) 63 

2.614. Elements in Bending 64 

**2.6140. Deflections 65 

*2.615. Elements as Columns 65 

2.7. FLAT RECTANGULAR PLY- 

WOOD PANELS 76 

2.70. Buckling Criteria 76 

2.71. General 76 



*2.710. Compression or Shear . 7G 

**2.711. Combined Compression (of 
Tension) and Shear Panel 
Edges Simply Supported 77 

2.72. Allowable Shear in Plywood 
Webs 96 

2.720. General ' 96 

*2.721. Allowable Shear Stresses 96 

2.722. Use of Figure 2-41 97 

*2.723. Buckling of Plywood Shear 

Webs 100 

2.73. Lightening Holes ' 100 

*2.74. Torsional Strength and 

Rigidity of Box Spars 100 

2.75. Plywood Panels Under Nor- 
mal Loads 100 

2.750. General 100 

2.751. Small Deflections 100 

2.752. Large Deflections 103 

2.76. Stiffened Flat Plywood Panels 103 
*2.760. Effective Widths in Com- 
pression 103 

*2.761. Compressive Strength 105 

*2.7610. Modes of Failure in Stiffened 

Panels 107 

*2.762. Bending 107 

2.8. CURVED PLYWOOD PANELS. ... 109 
**2.80. Buckling in Compression 109 

*2.81. Strength in Compression or 
Shear: or Combined Com- 
pression (or Tension) and 
Shear 109 

2.82. Circular Thin-Walled Ply- 
wood Cylinders 109 

2.820. Compression with Face Grain 
Parallel or Perpendicular to 
the Axis of the Cylinder. . . . 109 
*2.821. Compression with 45° Face 

Grain. Ill 

2.822. Bending Ill 

*2.823. Torsion .' Ill 

2.824. Combined Torsion and 

Bending Ill 

2.9. JOINTS 114 

2.90. Bolted Joints 114 

2.900. Bearing Parallel and Perpen- 
dicular to Grain 114 

2.901. Bearing at an Angle to the 
Grain 115 

2.902. Bearing in Woods other than 
Spruce 118 

2.903. Combined Concentric and 
Eccentric Loadings; Bolt 
Groups 118 

2.904. Bolt Spacings 118 



11 



2.9040. Spacing of Bolts Loaded 
Parallel to the Grain 119 

2.9041. Spacing of Bolts Loaded 
Perpendicular to the Grain. . 119 

2.9042. Spacing of Bolts Loaded at 

an Angle to the Grain 119 

2.9043. General Notes on Bolt Spacing. 119 
2.905. Effects of Reinforcing Plates . . 121 
2.900. Bushings 121 

2.907. Hollow Bolts 121 

2.908. Bearing in Plywood 122 

2.91. Glued Joints 122 



2.910. Allowable Stress for Glued 
Joints 122 

2.911. Laminated and Spliced Spars 
and Spar Flanges 1 22 

2.912. Glue Stress Between Wel> 

and Flange 122 

2.92. Properties of Modified 

Wood 122 

2.920. Detailed Test Data for 

Tables 2-13 and 2-14 123 

2.93. References 129 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



2.0. PHYSICAL CHARACTERISTICS OF WOOD. 

2.00. Anisotropy of Wood. Wood, unlike most other commonly used structural 
materials, is not isotropic. It is a complex structural material, consisting essentially 
of fibers of cellulose cemented together by lignin. It is the shape, size, and arrangement 
of these fibers, together with their physical and chemical composition that govern the 
strength of wood, and account for the large difference in properties along and across 
the grain. 

The fibers are long and hollow tubes tapering toward the ends, which are closed. 
Besides these vertical fibers, which are oriented with their longer dimension lengthwise 



L 




Figure 2-1.— Wood cellular structure. Drawing cf a highly magnified block of softwood measuring 
about one-fortieth inch vertically: it, transverse surface; rr, radial surface; tg, tangential surface; ar, 
annual rings; urn, summerwood; sp, springwood; tr, tracheids, or fibers; hrd, horizontal resin duct; 
far, fusiform wood ray; wr, wood rays; L, direction (longitudinal) of grain; R, direction radial to annual 
rings and perpendicular to grain direction; T, direction tangential to annual rings and perpendicular 

to grain direction; vrd, vertical resin duct. 

13 



14 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



of the tree and comprise the principal part of what is called wood, all species, except 
palms and yuccas, contain horizontal strips of cells known as rays, which are oriented 
radially and are an important part of the tree's food transfer and storage system. Among 
different species the rays differ widely in their size and prevalence. 

From the strength standpoint, this arrangement of fibers results in an anisotropic 
structure, that accounts for three Young's moduli differing by as much as 150 to 1, three 
shear moduli differing by as much as 20 to 1, six Poisson's ratios differing by as much as 
40 to 1, and other properties differing by various amounts. Not all of these wood 
properties have, as yet, been thoroughly evaluated. 

Figure 2-1 shows a diagrammatic sketch of the cellular structure of wood. Each 
year's growth is represented by one annual ring. The portion of the growth occurring 
in the spring consists of relatively thin-walled fibers, while that occurring during 'the 
later portion of the growing season consists of fibers having somewhat heavier walls. 
Thus, there is, for most woods, a definite line of demarcation between the growth 
occurring in successive years. The relation between the cellular structure of the wood 
and the three principal axes — longitudinal (L), tangential (T), and radial (R) — is indi- 
cated on the sketch. Figure 2-2 shows the relation between these axes and (a) the log, 




ra) LOO 




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Cc) Q(/A/?T£& 5l/C££ l/£W££P O/? ££&£ 0/?4 /A/ L(JMg£/? 

Figx t re 2-2. — Principal directions in wood and plywood. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



15 



(b) a flat-sawn board or rotary-cut veneer, and (c) an edge-grain board or quarter- 
sliced veneer. 

Table 2-1 — Variation oj wood strength properties with specific gravity 1 

i or 

S = strength at specific gravity g 
.s" = strength at specific, gravity g' 

(usually average values from 

column (2) of table 2-3). 



Static bending: 

Fiber stress at proportional limit 

Modulus of rupture 

Modulus of elasticity 

Work to maximum load 

Total work 

Impact bending: 

Fiber stress at proportional limit 

Modulus of elasticity 

Height of drop 



1 Values in this table apply only to variations within a species. See section 2.' 



1.50 
1.50 
1.25 
2.00 
2.25 



1.50 
1.25 
2.00 



Compression parallel to grain: 

Fiber stress at proportional limit 
Maximum crushing strength .... 
Modulus of elasticity 

Compression perpendicular to grain: 

Fiber stress at proportional limit 

Hardness — end, radial, tangential. . . . 



1.25 
1.25 
1.25 



2.50 
2.50 



2.01. Density or Apparent Specific Gravity. The substance of which wood is com- 
posed is actually heavier than water, its specific gravity being nearly the same for all 
species and averaging about 1.5. Since a certain proportion of the volume of wood is 
occupied by cell cavities, the apparent specific gravity of the wood of most species is 
less than unity. 

Relations between various strength properties and specific gravity have been 
developed (table 2-1) and are useful in estimating the strength of a piece of wood of 
known specific gravity. Considerable variability from these general relations is found, 
so that while they cannot be expected to give exact strength values, they do give good 
estimates of strength. Minimum permissible specific gravity values are listed in section 
2.10. 

The exponential values shown in table 2-1 apply to variation within a species. 
That is, they are to be used in determining the relation between the strength properties 
of pieces of the same species but of different specific gravity. For expressing the relation 
between the average strength properties of different species, the exponential values are 
somewhat lower. Such values are shown in table 14 of U. S. Department of Agriculture 
Technical Bulletin 479 (ref. 2-17). 

2.02. Moisture Content. Wood in the natural state in the living tree has con- 
siderable water associated with it. After being converted to lumber or other usable 
form, or during conversion, wood is commonly dried so that most of the water is removed. 

The water is associated with the wood in two ways, either absorbed in the cell walls, 
or as free water in the cell cavities. During drying, the free .water in the cell cavities 



16 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



is removed first, then that absorbed in the cell walls. The point at which all the water 
has been removed from the cell cavities while the cell walls remain saturated is known as 
the fiber-saturation point. For most species, the moisture content at fiber saturation 
is from 22 to 30 percent of the weight of the dry wood. 

Lowering the moisture content to the fiber-saturation point results in no changes 
in dimension or in strength properties. Lowering the moisture content below the fiber- 
saturation point, however, results in shrinkage and an increase in strength properties. 

Wood is a hygroscopic material, continually giving off or taking on moisture in 
accordance with the relative humidity and temperature to which it is exposed. Thus, 
while the strength of a piece of wood may be increased to a relatively high value by 
drying to a low moisture content, some of that increase may be lost if, in use, it is ex- 
posed to atmospheric conditions that tend to increase the moisture content. While 
paint and other coatings may be employed to retard the rate of absorption of moisture 
by wood, they do not change its hygroscopic properties, thus a piece of wood may be 
expected to come to the same moisture content under the same exposure conditions 
whether painted or unpainted. The time required will vary, depending upon whether 
or not it is coated. It is desirable, therefore, to design a structure on the basis of the 
strength corresponding to the conditions of use. 

Moisture content is generally expressed as a percentage of the dry weight of the 
wood. The percentage variation of wood strength properties for 1 percent change in 
moisture content is given in table 2-2. Since this variation is an exponential function, 
it is necessary that strength adjustments based on the percentage changes given in the 
table be made successively for each 1 percent change in moisture content until the total 
change has been covered. 

2.03. Shrinkage. Reduction of moisture content below the fiber-saturation point 
results in a change in dimension of the wood. Shrinkage in the longitudinal direction 
is generally negligible, but in the other two directions it is considerable. In general, 
radial shrinkage is less than tangential, the ratio between the two varying with the 
species. 

A quarter-sawed board will, therefore, shrink less in width but more in thickness 
than a flat-sawed board. The smaller the ratio of radial to tangential shrinkage, the 
more advantage is to be gained through minimizing shrinkage in width by using a quarter- 
sawed board. The smaller the difference between radial and tangential shrinkage, the 
less, ordinarily, is the tendency to check in drying and to cup with changes in moisture 
content. 

In general, woods of high specific gravity shrink and swell more for a given change 
in moisture content than do woods of low specific gravity. 

2.1. BASIC STRENGTH AND ELASTIC PROPERTIES OF WOOD. 

2.10. Design Values, Table 2-3. Strength properties of various species for use in 
calculating the strength of aircraft elements are presented in table 2-3. Their applica- 
bility to the purpose is considered to have been substantiated by experience. The- as- 
sumptions (see footnotes to table 2-3), made in deriving the values in table 2-3 from the 
results of standard tests (sec. 2.12) particularly that relating to "duration of stress", 
are, however, being reexamined in the light of recent data and additional studies are 
under way to further clarify the basis of design. Included is experimental work to further 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



17 



Table 2-2. — Percentage increase (or decrease) in wood strength properties for one percent decrease 

(or increase) in moisture content 1 







Static bending 




Com- 


















pres- 


















sion 


Com- 


Shear- 














parallel 


pres- 


ing 






Fiber 


Mod- 


Mod- 


Work 


to 


sion 


strength 


Hard- 


Species 


stress 


ulus 


ulus 


to 


grain, 


perpen- 


parallel 


ness 




at pro- 


of 


of 


maxi- 


maxi- 


dicular 


to 


(side) 




por- 


rup- 


elas- 


mum 


mum 


to 


grain 






tional 


ture 


ticity 


load 2 


crushing 


grain 








limit 








strength 








(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


_ 

(7 ) 


(o) 


( ■' ) 


H ardwoods: 3 




















8.9 


0.4 


3.6 


1.8 


8.3 


6.8 


5.1 


4.1 




4.1 


3 5 


1 4 


.4 


4.7 


4.8 


2.9 


2.4 


Basswood, American 


6.8 


"i.O 


9 O 


2.6 


6.5 


6.6 


4.2 


4.2 


Beech, American 


6.0 


4 7 


1 R 
1 .0 


2.0 


6.2 


5.3 


3.8 


3.6 




6.4 


o.u 


9 Q 


1.2 


7.1 


7.2 


5.0 


3.6 




6.0 


4.8 


2.0 


1.7 


6.1 


5.6 


3.6 


3.3 


Cherry, black 


6.6 


3.6 


1.1 


1.0 


6.0 


5.5 


3.5 


3.1 


Cottonwood 


5.8 


4.1 


2.5 


.1 


6.6 


5.7 


2.6 


1.8 


Elm rock 


4.7 


3.8 


2. 1 


- .3 


5.3 


6.1 


3.5 


2.8 


Hickory (true hickories) 


4.9 


4.8 


2.8 


- .7 


5.9 


6.6 


3.9 




Khava ("African mahogany") 


3.2 


2.5 


1.6 


- .G 


3.2 


3.0 


.4 


3.1 


Mahogany 


2.6 


1.3 


.8 


-2.9 


2.5 


3.9 




1.. 


Maple, sugar 


5.2 


4.4 


1 .4 


1.9 


5.7 


7.1 


3.9 


3.4 


Oak, commercial white ami red .... 


4.6 


4.4 


2.4 


1.7 


5.9 


4.4 


3.5 


1.8 


Sweetgum . 


6.7 


4.7 


2.2 


1.5 


6.1 


5.4 


3.5 


2.4 




5.8 


3.7 


1.4 


-2.6 


4.8 


6.3 


1.0 


1.0 


Yellowpoplar 


5.0 


4.6 


2.7 


1.9 


6.7 


4.8 


3.3 


2.4 


Softwoods (conifers) ^ 




















4.6 


4.0 


1.6 


1.8 


4.9 


5.1 


1.7 


2.3 




4.5 


3.7 


1.8 


1.9 


5.5 


5.0 


1.7 


2.9 


Fir, noble 


5.1 


4.7 


1.9 


3.2 


6.1 


5.5 


2.3 


3.1 


Hemlock, western 


4.7 


3.4 


1.4 


.7 


5.0 


3.7 


2.5 


2.0 




3.4 


2.1 


1.8 


-1.4 


4.3 


4.0 


.4 


1.5 


Pine, eastern white 


5.6 


4.8 


2.0 


2.1 


5.7 


5.6 


2.2 


2.2 


Pine, red 


8.0 


5.7 


2.2 


4.7 


7.5 


7.2 


3.9 


4.5 


Pine, sugar 


4.4 


3.9 


2.1 


.1 


5.4 


4.4 


3.7 


1.9 


Tine, western white 


5.3 


5.1 


2.2 


4.8 


6.5 


5.2 


2.5 


1.5 


Redeedar, western 


4.3 


3.4 


1.6 


1.3 


5.1 


5.1 


1.6 


' 2.3 


Spruce, red and Sitka 


4.7 


3.9 


1.7 


2.0 


5.3 


4.3 


2.6 


2.4 




5.8 


4.8 


1.9 


2.1 


6.5 


5.7 


3.7 


3.3 


White-cedar, northern 


5.4 


3.6 


1.8 


-1.5 


5.9 


2.3 


2.8 


3.0 


White-cedar, Port Orford 


5.7 


5.2 


1.6 


1.7 


6.2 


6.7 


2.2 


2.8 



1 Corrections to the strength properties should be made successively for each one percent change in moisture content 
until the total change has been covered. 

2 Negative values indicate a decrease in work to maximum load for a decrease in moisture content. 

3 For tension values see section 2.5411. 



explore the effect of rate of loading on the more important properties; to clarify the 
relations among rate of load application, duration of load, and strength; and to correlate 
these data with the load-time relations that may obtain in static testing and in air- 
plane flight. 

When tests of physical properties are made on additional species or on specially 
selected wood the results may be made comparable to those in table 2-3 by adjusting 



18 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



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STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



21 



them to 15 percent moisture content (in accordance with table 2-2) together with the 
appropriate use of the factors described in the footnotes to table 2-3. 

For notes on acceptable procedures for static tests and the correction of test results, 
see sections 2.12 and 3.01. 

2.100. Supplemental notes. 

2.1000. Compression perpendicular to grain. Wood does not exhibit a definite 
ultimate strength in compression perpendicidar to the grain, particularly when the load 
is applied over only a part of the surface, as it is by fittings. Beyond the proportional 
limit the load continues to increase slowly until the deformation and crushing become 
so severe as to damage seriously the wood in other properties. A factor of 1.33 was 
applied to average values of stress at proportional limit to get design values comparable 
to those for bending, compression parallel to grain, and shear as shown in table 2-3. 

2.1001. Compression parallel to grain. Available data indicate that the propor- 
tional limit for hardwoods is about 75 percent and for softwoods about 80 percent of 
the maximum crushing strength. Accordingly, design values for fiber stress at propor- 
tional limit were obtained by multiplying maximum crushing-strength values by a 
factor of 0.75 for hardwoods and 0.80 for softwoods. 

2.11. Notes on the Use of Values in Table 2-3. 

*2.110. Relation of design values in table 2-3 to slope of grain. The values given 
in table 2-3 apply for grain slopes as steep as the following: 
(a) For compression parallel to grain — 1 in 12. 

(£>) For bending and for tension parallel to grain — 1 in 15. When material is used 
in which the steepest grain slope is steeper than the above limits, the design values of 
table 2-3 must be reduced according to the percentages in table 2-4. 



Table 2-4. — Reduction in wood strength for various grain slopes. 





Corresponding design value, percent of value in table 2-3 






Static bonding 




Compression 


Tension 


Maximum slope of grain in the member 








parallel to 


parallel to 










grain 


grain 




Fiber stress 


Modulus 


Modulus of 


Maximum 


Modulus of 




at proportional 


of 


elasticity 


crushing 


rupture 




limit 


rupture 




strength 




1 in 15 


100 


100 

88 


100 




100 


1 in 12 


98 


97 


100 


85 


1 in 10 


87 


78 


91 


98 


75 


1 in 8 


78 


07 


84 


94 


60 



2.111. Tension parallel to grain. Relatively few data are available on the tensile 
strength of various species parallel to grain. In the absence of sufficient tensile-test 
data upon which to base tension design values, the values used in design for modulus 
of rupture are used also for tension. While it is recognized that this is somewhat con- 
servative, the pronounced effect of stress concentration, slope of grain (table 2-4) and 
other factors upon tensile strength makes the use of conservative values desirable. 

Pending further investigation of the effects of stress concentration at bolt holes, 
it is recommended that the stress in the area remaining to resist tension at the critical 
section through a bolt hole not exceed two-thirds the modulus of rupture in static 



22 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



bending when cross-banded reinforcing plates are used; otherwise one-half the modulus 
of rupture shall not be exceeded. 

2.112. Tension perpendicular to grain. Values of strength of various species in 
tension perpendicular to grain have been included for use as a guide in estimating the 
adequacy of glued joints subjected to such stresses. For example, the joints between 
the upper wing skin and wing framework are subjected to tensile stresses perpendicular 
to the grain by reason of the lift forces exerted on the upper skin surface. 

Caution must be exercised in the use of these values, since little experience is 
available to serve as a guide in relating these design values to the average property. 
Considering the variability of this property, however, the possible discontinuity or lack 
of uniformity of glue joints, and the probable concentration of stress along the of edges 
such joints, the average test values for each species have been multiplied by a factor of 
0.5 to obtain the values given in table 2-3. 

2.12. Standard Test Procedures. 

2.120. Static bending. In the static-bending test, the resistance of a beam to slow- 
ly applied loads is measured. The beam is 2 by 2 inches in cross section and 30 inches 
long and is supported on roller bearings which rest on knife edges 28 inches apart. Load 
is applied at the center of the length through a hard maple block inches wide, having 
a compound curvature. The curvature has a radius of 3 inches over the central 2}/g 
inches of arc, and is joined by an arc of 2-inch radius on each side. The standard place- 
ment is wjth the annual rings of the specimen horizontal and the loading block bearing 
on the side of the piece nearest the pith. A constant rate of deflection (0.1 inch per 
minute) is maintained until the specimen fails. Load and deflection are read simul- 
taneously at suitable intervals. 

Figure 2-3 (a) shows a diagrammatic sketch of the static-bending test set-up, and 
typical load-deflection curves for Sitka spruce and yellow birch. 

Data on a number of properties are obtained from this test. These are discussed 
as follows: 

2.1200. Modulus of elasticity (El). The modulus of elasticity is determined from 
the slope of the straight line portion of the graph, the steeper the line, the higher being 
the modulus. Modulus of elasticity is computed by 

P 7.3 p TZ 

483 J 4S P 6# K ' 



The standard static bending test is made under such conditions that shear deformations 
are responsible for approximately 10 percent of the deflection. Values of E L from tests 
made under such conditions and calculated by the formula shown do not, therefore, 
represent the true modulus of elasticity of the material, but an "apparent" modulus of 
elasticity. 

The use of these values of apparent modulus of elasticity in the usual formulas will 
give the deflection of simple beams of ordinary length with but little error. For I- and 
box beams, where more exact computations are desired, and formulas are used that take 
into account the effect of shear deformations, a "true" value of the modulus of elasticity 
is necessary and may be had by adding 10 percent to the values in table 2-3. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 




-MODULUS LINE 

^MAXIMUM 
LOAD 



SITKA 
SPRUCE 




MODULUS . ^ 


YELLOW 


LINE^i \ 

/ MAXIMUM^ 


BIRCH 


f LOAD 




/"PROPORTIONAL 




/ LIMIT 





TEST METHOD 



DEFLECT/ON (INCHES) 



(a) STA TIC BENDING 




^-MAXIMUM LOAD 


SITKA 




SPRUCE 


/ PROPORTIONAL 




I LIMIT 





^-MAXIMUM LOAD 


YELLOW 




BIRCH 


/ PROPORTIONAL ~~~~ 




I LIMIT 





TEST METHOD DEFORMATION (INCHES) 

(b) COMPRESSION PARALLEL TO GRAIN 








NO MAXIMUM 




LOAD OBTAINED 


\ PROPORTIONAL 


SITKA 


\ LIMIT 




SPRUCE 





NO MAXIMUM 


C 


LOAD OBTAINED 


/ ^PROPORTIONAL 




I LIMIT 






YELLOW 




BIRCH 



TEST METHOD 



DEFORMATION (INCHES) 
CO COMPRESSION PERPENDICULAR TO GRAIN 

Figure 2-3. — Standard test methods and typical load-deflection curves. 



24 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



2.1201. Fiber stress at proportional limit (F bp ). The plotted points from which 
the early portions of the curves of figure 2-3 (a) were drawn lie approximately on a 
straight line, showing that the deflection is proportional to the load. As the test progresses 
however, this proportionality between load and deflection ceases to exist. The point 
at which this occurs is known as the proportional limit. The corresponding stress in the 
extreme fibers of the beam is known as "fiber stress at proportional limit." Fiber stress 
at proportional limit is computed by 

P P Lc 1.5 P P L 

Fb *- 4 I~ bd> (2 - 2) 



2.1202. Modulus of rupture (F h „). Modulus of rupture is computed by the same 
formula as was used in computing fiber stress at proportional limit, except that maxi- 
mum load is used in place of load at proportional limit. Since the formula used is based 
upon an assumption of linear variation of stress across the cross section of the beam, 
modulus of rupture is not truly a stress existing at time of rupture, but is useful in find- 
ing the load-carrying capacity of a beam. 

2.1203. Work to maximum load. The energy absorbed by the specimen up to the 
maximum load is represented by the area under the load-deflection curve from the 
origin to a vertical line through the abscissa representing the maximum deflection at 
which the maximum load is sustained. It is expressed, in table 2-3, in inch-pounds per 
cubic inch of specimen. Work to maximum load is computed by 

„ 7 , , D area under curve to P max . ,~ 
Work to P max . = -^-^ (2:3) 

2.121. Compression parallel to grain. In the compression-parallel-to-grain test, 
a 2- by 2- by 8-inch block is compressed in the direction of its length at a constant rate 
(0.024 inch per minute). The load is applied through a spherical bearing block, pref- 
erably of the suspended self-aligning type, to insure uniform distribution of stress. On 
some of the specimens, the load and the deformation in a 6-inch central gage length are 
read simultaneously until the proportional limit is passed. The test is discontinued 
when the maximum load is passed and the failure appears. 

Figure 2-3 (b) shows a diagrammatic sketch of the test set-up, and typical load- 
deflection curves for Sitka spruce and yellow birch. Data on a number of properties 
are obtained from this test. These are discussed as follows: 

2.1210. Modulus of elasticity (£/,, ). The modulus of elasticity is determined from 
the slope of the straight-line portion of the graph, the steeper the line the higher the 
modulus. The modulus of elasticity is computed by 

K - i',;. < 2:4) 

The value of the modulus of elasticity so determined corresponds to the "true" 
value of modulus of elasticity discussed under static bending. Values of the modulus of 
elasticity from compression-parallel-to-grain tests are not published but may be approxi- 
mated by adding 10 percent to the apparent values shown under static bending in table 
2-3. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



25 



2.1211. Fiber stress at proportional limit (F CP )- The plotted points from which 
early portions of the curves of figure 2-3 (b) were drawn lie approximately on a straight 
line, showing that the deformation within the gage length is proportional to the load 
The point at which this proportionality ceases to exist is known as the proportional 
limit and the stress corresponding to the load at proportional limit is the fiber stress at 
proportional limit. It is calculated by 

Fc P = -f- (2:5) 

2.1212. Maximum crushing strength (F IU ). The maximum crushing strength is 
computed by the same formula as used in computing fiber stress at proportional limit ex- 
cept that maximum load is used in place of load at proportional limit. 

2.122. Compression perpendicular to grain. The specimen for the compression- 
perpendicular-to-grain test is 2 by 2 inches in cross section and 6 inches long. Pressure 
is applied through a steel plate 2 inches wide placed across the center of the specimen 
and at right angles to its length. Hence, the plate covers one-third of the surface. The 
standard placement of the specimen is with the growth rings vertical. The standard 
rate of descent of the movable head is 0.024 inch per minute. Simultaneous readings 
of load and compression are taken until the test is discontinued at 0.1-inch compression. 

Figure 2-3 (c) shows a diagrammatic sketch of the test set-up, and typical load- 
deflection curves for Sitka spruce and yellow birch. 

The principal property determined is the stress at proportional limit (F cp t) which 
is calculated by 

p _ Load at proportional limit ^.g 
cp Width of plate X width of specimen 

Tests indicate that the stress at proportional limit when the growth rings are placed 
horizontal does not differ greatly from that when the growth rings are vertical. For 
design purposes, therefore, the values of strength in compression perpendicular to grain 
as given in table 2-3 may be used regardless of ring placement. 

2.123. Shear parallel to grain (F SII ). The shear-parallel-to-grain test is made by 
applying force to a 2-by 2-inch lip projecting % inch from a block 2^2 inches long. The 
block is placed in a special tool having a plate that is seated on the lip and moved down- 
ward at a rate of 0.015 inch per minute. The specimen is supported at the base so that 
a J^-inch offset exists between the outer edge of the support and the inner edge of the 
loading plate. 

The shear tool has an adjustable seat in the plate to insure uniform lateral distri- 
bution of the load. Specimens are so cut that a radial surface of failure is obtained in 
some and a tangential surface of failure in others. 

The property obtained from the test is the maximum shearing strength parallel 
to grain. It is computed by 




(2:7) 



The value of F su as found when the surface of failure is in a tangential plane does 
not differ greatly from that found when the surface of failure is in a radial plane, and 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



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STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



27 



the two values have been combined to give the values shown in column 14 of table 2-3. 

2.124. Hardness. Hardness is measured by the load required to embed a 0.444- 
inch ball to one-half its diameter in the wood. (The diameter of the ball is such that its 
projected area is one square centimeter.) The rate of penetration of the ball is 0.25 inch 
per minute. Two penetrations are made on each end, two on a radial, and two on a 
tangential surface of the specimen. A special tool makes it easy to determine when the 
proper penetration of the ball has been reached. The accompanying load is recorded 
as the hardness value. 

Values of radial and tangential hardness as determined by the standard test have 
been averaged to give the values of side hardness in table 2-3. 

2.125. Tension perpendicular to grain (F, u r). The tension-perpendicular-to-grain 
test is made to determine the resistance of wood across the grain to slowly applied 
tensile loads. The test specimen is 2 by 2 inches in cross section, and 2^ inches in overall 
length, with a length at midheight of 1 inch. The load is applied with special grips, the 
rate of movement of the movable head of the testing machine being 0.25 inch per 
minute. Some specimens are cut to give a radial and others to give a tangential surface 
of failure. 

The only property obtained from this test is the maximum tensile strength perpen- 
dicular to grain. It is calculated from the formula 

F tuT = ^Y 1 < 2:8) 

Tests indicate that the plane of failure being tangential or radial makes little 
difference in the strength in tension perpendicular to grain. Results from both types 
of specimens have, therefore, been combined to give the values shown in table 2-3. 

2.13. Elastic Properties Not Included in Table 2-3. Certain elastic properties use- 
ful in design are not included in table 2-3. The data in table 2-3 are, in general, based 
on large numbers of tests, while the data on the additional elastic properties are based on 
relatively few tests. Available data on these properties are included in table 2-5. 

2.130. Moduli of elasticity perpendicular to grain (Et, £/?). The modulus of elas- 
ticity of wood perpendicular to the grain is designated as Et when the direction is tangen- 
tial to the annual growth rings, and Er when the direction is radial to the annual growth 
rings. Tests have been made to evaluate these elastic properties for only a very few 
species (table 2-5), and, until further information is available, it is recommended that 
the ratios of Et/El and Er/El be taken as 0.045 and 0.085, respectively, for all species 
not listed in the tables. Values of El are given in table 2-3. 

*2.131. Moduli of rigidity (Glt, Glr, Grt)- The modulus of elasticity in shear, 
or the modulus of rigidity as it is called, must be associated with shear deformation in 
one of the three mutually perpendicular planes defined by the L, T, and R directions, 
and with shear stresses in the other two. The symbol for modulus of rigidity has sub- 
scripts denoting the plane of deformation. Thus the modulus of rigidity Glt refers to 
shear deformations in the LT plane resulting from shear stresses in the LR and RT 
planes. Values of these moduli for a few species are given in table 2-5. For other species 
not listed, it is recommended that the ratios Glt/El =0.05, Glr/El, = 0.06, and 
Grt/El = 0.01 be used in evaluating the various moduli of rigidity. 



28 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



*2.132. Poisson's ratios (\x). The Poisson's ratio relating to the contraction in 
the T direction under a tensile stress acting in the L direction, and thus normal to the 
RT plane, is designated as [Ilt', V-lr, V-rt, ^rl, [ltr, and \xtl have similar significance, 
the first letter of the subscript in each relating to the direction of stress and the second 
to the direction of the lateral deformation. The two letters of the subscript may be 
interchanged without changing the meaning when G is considered but the same is not 
true for \x. Information on Poisson's ratios for wood is meager and values for only a 
few species are given in table 2-5. 

2.14. Stress-strain relations. (See section 2.56.) 

2.2. COLUMNS. 

2.20. Primary Failure. The allowable stresses for solid wood columns are given 
by the following formulas: 



Long columns 



10 ^ . 

9 



(t) 



(2:9) 



L\ V 15E L 

Feu 



(-) = 

V p /cr 



Short columns (ref. 2-20) 



where: K = (-—) 

\ a /cr 



These formulas are reproduced graphically in figure 2-4 for solid wood struts of a 
number of species. 

2.21. Local Buckling and Twisting Failure. The formulas given in section 2.20 
do not apply when columns with thin outstanding flanges or low torsional rigidity are 
subject to local buckling or twisting failure. For such cases, the allowable stresses are 
given by the following formulas : 

Local buckling (torsionally rigid columns) 

F c = 0.07 E L (^) 2 psi (when p6) (2:11) 

Twisting failure (torsionally weak columns) 

F- = 0.044 E L (A' psi (when ^>5) (2:12) 

When the width-thickness ratio (b/t) of the outstanding flange is less than the 
values noted, the column formulas of section 2.20 should be used. Failure due to local 
buckling or twisting can occur only when the critical stress for these types of failure is 
less than the stress required to cause primary failure. For unconventional shapes, tests 
should be conducted to determine suitable column curves (ref. 2-32). 



STRENGTH OP WOOD AND PLYWOOD ELEMENTS 



29 




o 



isd Ml S S3 HIS NWniOD 319VM011V- 7 J 



30 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



2.22. Lateral Buckling. When subjected to axial compressive loads, beams will 
act as columns tending to fail through lateral buckling. The usual column formulas 
(2:9 and 2:10) will apply except that when two beams are interconnected by ribs so that 
they will deflect together (laterally), the total end load carried by both beams will be 
the sum of the critical end loads for the individual beams. 

The column lengths will usually be the length of a drag bay in a conventional wing. 
A restraint coefficient of 1.0 will be applicable unless the construction is such that addi- 
tional restraint is afforded by the leading edge or similar parts. Certain rules for such 
conditions will be found in the requirements of the certificating or procuring agencies. 

2.3. BEAMS. 

2.30. Form Factors. When other than solid rectangular cross sections are used for 
beams, (I-beams or box beams), the static-bending strength properties given in table 
2-3 must be multiplied by a "form factor" for design purposes. This form factor is the 
ratio of either the fiber stress at proportional limit or the modulus of rupture (in bending) 
of the particular section to the same property of a standard 2-inch square specimen 
of that material. The proportional limit form factor (FF P ) is given by the formula: 

FF P = 0.58+0.42 (k (2:13) 

and the modulus of rupture form factor (FF U ) by the formula: 

FF U = 0.50+0.50 (K (2:14) 

where 

b' = tota web thickness 

b = total flange width (including any web(s)) 
K = constant obtained from figure 2-5. 

Formulas 2:13 and 2:14 cannot be used to determine the form factors of sections 
in which the top and bottom edges of the beam are not perpendicular to the vertical 
axis of the beam. In such cases, it is first necessary to convert the section to an equivalent 
section whose height equals the mean height of the original section, and whose width 
and flange areas equal those of the original section, as shown in figure 2-5. The fact 
that the two beams of each pair shown in figure 2-5 developed practically the same 
maximum load in test demonstrates the validity of this conversion (ref. 2-16 and 2-21). 

Tests have indicated that the modulus of rupture which can be developed by a 
beam of rectangular cross section decreases with the height. Sufficient data are not 
available to permit exact evaluation of the reduction as the height increases, but where 
deep beams of rectangular cross section are to be used, thought should be given to the 
reduction of the value for modulus of rupture given in table 2-3. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



31 



35 



5 



15 




ioo 



£=7.5£ ± = &33 



c d 
L-4.73 ± = 5.33 



o- Maximum load = 3200 lb. '■*» f*"~^~i , f — 




£ = 4.73 
FFu= .86 FF V = .74 
FF V ±= 357 FF V ± = 3.50 FF V ± = 6.7/ FF V ±,6.76 



± = 9.88 
FF V = .68 



±= 10.40 
FF U = .65 



Figure 2-5. — Form-factor curve and equivalent beam sections. 



32 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



2.31. Torsional Instability. It Is possible for deep thin beams to fail through 
torsional instability at loads less than those indicated by the usual beam formula. Ref- 
erence 2-22 gives formulas for calculating the strength of such beams for various condi- 
tions of end restraint. However, in view of the difficulty of accurately evaluating the 
modulus of rigidity and end-fixity, it is always advisable to conduct static tests of a 
typical specimen. This will apply to cases in which the ratio of the moment of inertia 
about the horizontal axis to the moment of inertia about the vertical axis exceeds approxi- 
mately 25 (ref. 2-21 and 2-22). 

2.32. Combined Loadings. 

2.320. General. Because of the variation of the strength properties of wood with 
the direction of loading with respect to the grain, no general rules for combined loadings 
can be presented, other than those for combined bending and compression given in 
section 2.321, and those for combined bending and tension given in section 2.322. When 
unusual loading combinations exist, static tests should be conducted to determine the 
desired information. 

2.321. Bending and compression. When subjected to combined bending and 
compression, the allowable stress for spruce, western hemlock, noble fir, and yellow- 
poplar beams can be determined from figure 2-6; that for Douglas-fir beams can be 
determined from figure 2-7. The charts are based on a method of analysis developed by 
the Forest Products Laboratory (ref. 2-22 and 2-29). 

The curves of figures 2-6 and 2-7 are based on the use of a second-power parabola 
for columns of intermediate length. The use of these curves has given acceptable results, 
but later data on columns under compressive loading only has demonstrated that the use 
of a fourth-power parabola for columns of intermediate length, as in figure 2-4, is per- 
missible. New combined-loading curves, based on the use of a fourth-power parabola 
will be presented in connection with other contemplated revisions. On these figures, 
the horizontal family of curves indicates the proportional limit under combined bending 
and compression, and the vertical family the effect of various slenderness ratios on bend- 
ing. The allowable stress, F bc , under combined load is found as follows : 

(1) For the cross section of the given beam, find the proportional limit in bending 
and the modulus of rupture from the ratios of compression-flange thickness to total 
depth and of web thickness to total width, locating points such as A and B. - 

(2) Project points A and B to the central line, obtaining such points as C and D. 

(3) Locate a point such as E, indicating the proportional limit of the given section 
under combined bending and compression. This point will be at the intersection of the 
curve of the "horizontal" family through C and the curve of the slenderness ratio cor- 
responding to the distance between points of inflection. 

(4) Draw ED. 

(5) Locate F on ED, with an abscissa equal to the computed ratio of bending to 
total stress. The ordinate of F represents the desired value of the allowable stress. 

The following rules should be observed in the use of figures 2-6 and 2-7: 

(1) The length to be used in computing the slenderness ratio, L/p should be de- 
termined as follows : 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



33 



«o ^ "J 




34 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



(a) If there are no points of inflection between supports, L should be taken as the 
distance between supports. 

(6) If there are two points of inflection between supports, L should be taken as the 
distance between these points of inflection when calculating the allowable strength of 
any section included therein. 

(c) When calculating the allowable strength of a section between a point of in- 
flection and an intermediate support of a continuous beam, L should be taken as the 
distance between the points of inflection adjacent to the support on either side. 

(d) When investigating a section adjacent to an end support, L should be taken 
as twice the distance between the support and the adjacent point of inflection, except 
that it need not exceed the distance between supports. 

(2) In computing the value of p for use in determining the slenderness ratio, 
L/p, filler blocks should be neglected and, in the case of tapered spars, the average value 
should be used. 

(3) In computing the modulus of rupture and the proportional limit in bending, 
the properties of the section being investigated should be used. Filler blocks may be 
included in the section for this purpose. When computing the form factor of box spars, 
the total thicknesses of both webs should be used. 

2.322. Bending and tension. When tensile axial loads exist, the maximum com- 
puted stress on the tension flange should not exceed the modulus of rupture of a solid 
beam in pure bending. Unless the tensile load is relatively large, the compression flange 
should also be checked, using the modulus of rupture corrected for form factor. 

2.33. Shear Webs. See section 2.72. 

2.34. Beam Section Efficiency. In order to obtain the maximum bending efficiency 
of either I- or box beams, the unequal flange dimensions can be determined by first 
designing a symmetrical beam of equal flanges. The amount of material to be trans- 
ferred from the tension side to the compression side, keeping the total cross-sectional 
area, height and width constant, is given by the following equation (ref. 2-21) : 



x 



Abh 2 -VA 2 b 2 h 4 -4:AI s bhwD 
2wDbh 



(2:15) 



where : 



A = total area of the cross section 

b = total width 

h = total depth 

w = width of flange 

D = clear distance between flanges 

I s = moment of inertia of the symmetrical section 

x = thickness to be taken from tension flange and 



added to compression flange. 



In using this equation, the following procedure is to be followed : 
(a) Determine the section modulus required. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



35 




Nl OS" if 3d ff7 JO SaNVMOHl Nl **J fttiflS 319VM0nV 



36 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



(b) Determine the sizes of flanges of equal size to give the required section modulus. 

(c) Using equation (2:15), compute the thickness of material to be transferred 
from the tension flange to the compression flange. The procedure thus far will result 
in a section modulus greater than required. To obtain a beam of the required section 
modulus, either (d) or (e) may be followed. 

(d) Calculate the ratio of depth of tension flange to compression flange and design 
a section having flanges with this ratio and the required section modulus, or 

(e) Carry out steps (a), (6), and (c) starting with a symmetrical section having a 
section modulus less than that required until an unsymmetrical section having the re- 
quired section modulus is obtained. 

(/) Beams designed according to the foregoing procedure should always be checked 
for adequacy of glue area between webs and tension flange. This consideration may 
govern the thickness of the tension flange. 

2.4. TORSION. 

2.40. General. The torsional deformation of wood is related to the three moduli 
of rigidity, Glt, Glr, and Grt- When a member is twisted about an axis parallel to the 
grain, Grt is not involved; when twisted about an axis radial to the grain direction, 
Glt is not involved; when twisted about an axis tangential to the grain direction, Glr 
is not involved. No general relationship has been found for the relative magnitudes of 
G L r, Glt, and G RT . (Table 2-5). 

2.41. Torsional Properties. The "mean modulus of rigidity" (G) taken as V\?> of 
El, may be safely used in the standard formulas for computing the torsional rigidities 
and internal shear stresses of solid wood members twisted about an axis parallel to the 
grain direction. Torsion formulas for a number of simple sections are given in table 2-6. 
For solid-wood members the allowable ultimate torsional shear stress (F st ) may be taken 
as the allowable shear stress parallel to the grain (column 14 in table 2-3) multiplied by 
1.18 that is, F s( = 1.18 F su . The allowable torsional shear stress at the proportional 
limit may be taken as two-thirds of F st . The torsional strength and rigidity of box 
beams having plywood webs are given in section 2.74. 



T\ble 2-6. — Formulas for torsion on symmetrical sections 



Section 



Angle of twist in radians 



Maximum shear stress 



Circular tube 



Circle. 



Ellipse 





fs =— at ends of short diameter. 

■nab 2 



TD 



G 7ra = & 3 



Rectangle 3 



Square' 2 




fs = — - (approx.) 



fs = ^ V5a-\-9b) a( . jjjjdpoint of long side. 



1 2a =major axis: 2b =minor axis, 

2 2a =side of square. 

3 2a = long side, 2b = short side. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



37 



2.5. BASIC STRENGTH AND ELASTIC PROPERTIES OF PLYWOOD. 

2.50. General. Plywood is usually made with an odd number of sheets or plies of 
veneer with the grain direction of adjacent plies at right angles. Depending upon the 
method by which the veneer is cut, it is known as rotary-cut, sliced, or sawed veneer. 
Generally, the construction is symmetrical ; that is, plies of the same species, thickness, 
and grain direction are placed in pairs at equal distances from the central ply. Lack of 
symmetry results in twisting and warping of the finished panel. The disparity between 
the properties of wood in directions parallel to and across the grain is reduced by reason 
of the arrangement of the material in plywood. By placing some of the material with 
its strong direction (parallel to grain) at right angles to the remainder, the strengths in 
the two directions become more or less equalized. Since shrinkage of wood in the longi- 
tudinal direction is practically negligible, the transverse shrinkage of each ply is re- 
strained by the adjacent plies. Thus, the shrinking and swelling of plywood for a given 
change in moisture content is less than for solid wood. 




fa) Ptywooo fe) sr/?A/A/ (cjr stress 

Figure 2-8. — Three-ply plywood beam in bending. 
Table 2-7. — Veneer species for aircraft plywood 



Group I (high density) 1 ' 2 


Group II (medium density) 2 


Group III (low density) 5 


American beech 


Birch (Alaska and paper) 


Basswood 


Birch (sweet and yellow) 


Khaya species (so-called "African mahogany") 


Yellowpoplar 


Maple (.hard) 


Southern magnolia 


Port Orford white-cedar 


Pecan 


Mahogany (from tropical America) 


Spruce (red, Sitka, and white) 




Maple (soft) 


(quarter-sliced) 




Sweetgum 


Ponderosa pine (quarter-sliced) 




Water tupelo 


Sugar pine 




Black walnut 


Noble fir (quarter-sliced) 




Douglas-fir (quarter-sliced) 


Western hemlock (quarter-sliced) 




American elm (quarter-sliced) 


Redwood (quarter-sliced) 




Sycamore 





1 Where hardness, resistance to abrasion, and high strength of fastening are desired, Group I woods should be used 
for face stock. 

2 Where finish is desired, or where the plywood is to be steamed and bent into a form in which it is to remain, species 
of Group I and II should be used. 

3 Group III species are used principally for core stock and cross-banding. However, where high bending strength or 
freedom from buckling at minimum weight is desired, plywood made entirely from species of Group III is recommended. 



38 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



The tendency of plywood to split is considerably less than for solid wood as a 
result of the cross-banded construction. While many woods are cut into veneer, those 
species which have been approved for use in aircraft plywood are listed in table 2-7. 

2.51. Analysis of Plywood Strength Properties. The analysis of the strength and 
elastic properties of plywood is complicated by the fact that the elastic moduli of ad- 
jacent layers are different. This is illustrated in figure 2-8 for bending of a three-ply 
panel. Assuming that strain is proportional to distance from the neutral axis, stresses 
on contiguous sides of a glue joint will be different by reason of the difference in the 
modulus of elasticity in adjacent layers. This results in a distribution of stress across 
the cross section as shown in figure 2-8 (c). Similar irregular stress distribution will be 
obtained for plywood subjected to other types of loading. 

From this it may be seen that the strength and elastic properties of plywood are 
dependent not only upon the strength of the material and the dimensions of the mem- 




f/:2:/j j-^zr^/.y.vj 




s-/=>i y^/;2. 2:2:/) s-pl y (/:/:/:/:/) 

Figure 2-9. — Typical plywood constructions. Arrows indicate grain direction of each ply. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



39 



ber, as for a solid piece, but also upon the number of plies, their relative thickness, and 
the species used in the individual plies. In addition, plywood may be used with the 
direction of the face plies at angles other than 0° or 90° to the direction of principal 
stress and, in special cases, the grain direction of adjacent plies may be oriented at angles 
other than 90°. 

In general, plywood for aircraft use has the grain direction (the longitudinal direc- 
tion) of adjacent plies at right angles. The strength and elastic properties of the plywood 
are dependent upon the properties of solid wood along and across the grain as illustrated 
in figure 2-9. 

Considerable information (table 2-3) on the properties of wood parallel to the grain 
is available, but the data on properties across-the-grain are less complete. Sufficient 
data are available, however, so that the elastic properties of wood in the two directions 
can be related with reasonable accuracy to the plywood properties. On this basis formulas 
are given which will enable the designer, knowing the number, relative thickness and 
species of plies, to compute the properties of plywood from the data given in table 2-3. 

The formulas given are only for plywood having the grain direction of adjacent plies 
at right angles and are applicable only to certain directions of stress. The limitations 
on the angle between the face grain and the direction of principal stress have been noted 
in each section. The formulas are intended for use only in these cases, and the inter- 
polation must not be used to obtain values for intermediate angles unless specific in- 
formation on these angles is given. Computed values of certain of the strength and 
elastic properties for many of the commonly used species and constructions of plywood 
are given in section 2.540. 

2.52. Basic Formulas. For purposes of discussion, plywood structural shapes may 
be conveniently separated into two groups : (a) elements acting as prisms, columns, and 
beams, and (b) panels. The fundamental difference between these two groups is that, in 
group (a) the plywood is supported or restrained only on two opposite edges, while in 
group (b) the plywood is supported or restrained on more than two edges. It is essential 
that this fundamental difference between the two groups be kept in mind during the 
application of the formulas 2 given here and in later sections. 

(1) The effective moduli of elasticity of plywood in tension or compression are : 
E a — measured parallel to side a for panels (sec. 2.710) 
Eb — measured perpendicular to side a for panels (sec. 2.710) 
E w — measured parallel to (with) the face grain 
E x — measured perpendicular to (across) the face grain 
and are determined as 



! When computing the various moduli of elasticity ior plywood of balanced construction and all plies of the same 
species, the following relationship will be found helpful: 

E L +E T = E a +E b =E 1 +E s =E w +Es=E fw +E fI 
If the veneers are quarter-sliced rather than rotary-cut, the term Ex should be replaced by Er. 




tl 



(2:16) 



■ 

40 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



where : 

A = total cross section area. 
Ai = axea, of i' h ply. 

E; = modulus of elasticity of ply measured in the same direction as the perti- 
nent desired E (as E a , Eb, E w , or E x ). The value of Ei is equal to 1.1 El 
(table 2-3), or Et, or Er, (table 2-5) as applicable. 
(2) The effective moduli of elasticity of plywood in bending are : 
Ei — measured parallel to side a for panels. 
Ei — measured perpendicular to side a for panels. 
E fw — measured parallel to (with) the face grain, 
/^-—measured perpendicular to (across) the face grain and 
are determined as 

i =n 

= y\ Ei h (2:17) 

/_ 

i = l 

Where : 

Er — as defined under (1). 
7= moment of inertia of the total cross section about the centerline, measured 
in the same direction as the pertinent desired E (namely, E x , E2, E fw , or E fx ). 
7,= moment of inertia of the i' h ply about the neutral axis of the same total cross 
section. For symmetrically constructed plywood, the neutral axis to be used 
in determining I{ will be the centerline of the cross section. For unsymmetrical 
plywood constructions, the neutral axis is usually not the centerline of the 
geometrical section. In this case the distance from this neutral axis to the 
extreme compression fiber is given by the equation: 

AiEid 

(2:18) 

AiEi 

i = l~ 



% 


= n 


\ 

/ 


i 


= 1 


i 


= n 


\ 
/ 



where : 

c, = distance from the extreme compression fiber to the center of the i th ply. 
(3) In calculating the bending strength (not stiffness) of plywood strips in bending 
having the face grain direction perpendicular to the span, a modulus E' fx , similar to 
E fx is to be used. For plywood made of five or more plies, the use of E fx for E' fx in 
strength calculations will result in but relatively small error. The value of E' fx may be 
calculated in the same manner as that used in calculating E fx except that the effect of 
the outer ply on the tension side is neglected. The location of the neutral axes used in 
calculating E fx and E' fx will be different. The value of E' fx may also be calculated from 
the following formula: 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



41 



E'^E fx +^ (c'-^+^-^r- (C^) 2 (2.19; 



where: 

" tE x 

1 l, Ei 

c = 



tE r 1 

tf Et 

= distance from neutral axis to extreme fiber of the outermost longitudinal ply. 
Et pertains to the species of the face ply. 

*(4) The modulus of rigidity (modulus of elasticity in shear) of solid wood involves 
the sheer moduli Glt, Glr, and Gut- 

As mentioned in section 2.131, little information is available on this elastic property, 
and a "mean" modulus of ridigity is ordinarily used for wood. Similarly for plywood, 
a value of modulus of rigidity based on the "mean" modulus of rigidity for solid wood 
may be used. 

For plywood (all plies the same species) having the face grain parallel or perpendicu- 
lar to the direction of principal shearing stress, the modulus of rigidity may be taken 
the same as for solid wood. For plywood having the face grain at 45° to the direction 
of principal shearing stress, the modulus of rigidity may be taken as five times the "mean" 
modulus of rigidity for solid wood (sec. 2.41). Thus, the modulus of rigidity for 45° ply- 
wood is approximately % of the bending modulus of elasticity parallel to the grain of 
solid wood (sec. 2.56) as given in table 2-3. 

The theoretical treatment of the elastic properties of plywood involves the moduli 
of rigidity G wx and G fwx . The apparent modulus of rigidity in the plane of the plywood is 

i = n 

G wx =-\ CnU (2:20) 

/ 
i = l 

where the summation is taken over all plies in a section perpendicular to either the a or b 
directions using the modulus of rigidity in each ply in the wx plane. 
When the plywood is made of a single species of wood, 
G wx = Glt for rotary-cut veneer. 
G wx = Glr for quarter-sliced veneer 
The apparent modulus of rigidity of plywood for use in formulas involving the 
bending of plywood plates into double curvature is 

i = n 

G /wx =— y QL+t^Gi (2:21) 

/ 

i=l 

where yi = distance from the neutral axis to the center of the i th ply. 

*(5) Poisson's ration ((x). Although there is very little information available on 
the values of Poisson's ratios for plywood, a brief summary of their significance is given. 



42 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



The effective Poisson's ratio of plywood in tension or compression (no flexure) is the 
ratio of the contraction along the x direction to extension along the w direction due to 
tensile stress acting in the w direction and thus normal to the xt plane, or 

i = n 

^•* = 7"p~/ U{E x )i ([k wx )i (2:22) 

tE * i = l 



modulus of elasticity of the i' h ply in the x direction. 

Poisson's ratio of contraction along the x direction to extension in the w 
direction due to a tensile stress acting in the w direction and thus normal 
to the xt plane of the i th ply. 

i =n 
i = l 

If all plies are of the same species of rotary-cut veneer 

\x wx = El v-tl/E x 

\j. X w=El \>-tl/E w 
If all plies are of the same species of quarter-sliced veneer 

\>. wx = El v-rl/E x 

^ tu =El v-rl/E w 

These formulas give close approximations of the apparent Poisson's ratios in these 
two directions when the stress is simple tension or compression. For more accurate 
formulas than 2 :22 and 2 :23 see reference 2-25. For Poisson's ratio at an angle to the 
grain see section 2.56. 

*2.5 3. Approximate Methods for Calculating Plywood Strengths. Table 2-8 gives 
some approximate methods of calculating the various strength properties of plywood. 
These simplified methods will be found very useful in obtaining estimates on the strength 
of plywood, but cannot be relied upon to give results which are comparable to those 
obtained with the more accurate methods. 

2.54. Moisture-Strength Relations for Plywood. 

2.540. General. The design values given in the plywood strength-property tables 
2-9 and 2-10 were calculated from the strength properties of solid wood as given in 
table 2-3. 

Adjustment factors by which strength properties of solid wood may be corrected 
for moisture content are shown in table 2-2. For plywood, moisture corrections are 
dependent on many variable factors, such as grain direction, combinations of species, 
and relative thicknesses of plies in each direction, so that any rational method of cor- 
rection is quite laborious. An approximate method for making moisture corrections to 
plywood is given in the succeeding sections. 

2.541. Approximate methods for making moisture corrections for plywood 
strength properties. A limited number of compression, bending, and shear tests of 
spruce and Douglas-fir plywood of a few constructions at moisture content values 



where : 

(E x )i = 

(|*wz)« = 



Similarly 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



43 



ranging approximately from 6 to 15 percent has indicated that use of the following 
simplified methods of correcting plywood strength properties will be satisfactory. 

2.5410. Moisture corrections for plywood compressive strength (0° or 90° to 
face grain direction). Moisture adjustments to the compressive strength of plywood, 
either parallel or perpendicular to the face grain direction, may be made by direct use of 
the correction constants given in column (6) of table 2-2. 

When more than one species is used in the plywood, the correction constant should 
be taken for that species having its grain direction parallel to the applied load. 

When plies of two species have their grain direction parallel to the applied load, the 
plywood correction constant should be determined by taking the mean value of the cor- 
rection constants for the two species based on the relative areas of the longitudinal plies 
of each. 

*2.54ll. Moisture correction for plywood tensile strength (0° or 90° to face 
grain direction). Data on the effect of moisture on the tensile strength of plywood 
are lacking. Limited data indicate that the effect on the tensile strength of wood is about 
one-third as great as on modulus of rupture. The suggested procedure for adjusting the 
tensile strength of plywood is to follow that for compressive strength as given in the 
preceding section, using one-third of the correction factors given for modulus of rupture 
in column 3 of table 2-2. 

*2.5412. Moisture corrections for plywood shear strength (0° or 90° to face 
grain direction). Moisture adjustments to the shear strength of plywood, either 
parallel or perpendicular to the face grain direction, F swx , may be made by direct use 
of empirical correction constants equal to those given in column (8) of table 2-2 for 
shear. The use of such moisture adjustment to the shear strength of plywood is not 
applicable when a moisture content of less than 7 percent is involved. 

When more than one species is used, the correction constant should be determined 
on the basis of the relative areas of each species, considering all plies. 

2.5413. Moisture corrections for plywood compressive strength (any angle to 
face grain direction). The compression strength of plywood at any moisture content, 
and at any angle to the face grain direction, may be found by use of equation 2:19 after 
first correcting the compression terms F cuw and F cux in accordance with section 2.5410. 

2.5414. Moisture corrections for plywood tensile strength (any angle to face 
grain direction). The tension strength of plywood at any moisture content, and at any 
angle to the face grain direction, may be found by use of equation 2:50 after first cor- 
recting the tension terms F tuw and F tux in accordance with section 2.5411, and the shear 
term F swx in accordance with section 2.5412. 

2.5415. Moisture corrections for plywood shear strength (any angle to face grain 
direction). The shear strength of plywood at any nioisture content, and at any angle 
to the face grain direction, may be found by use of equations 2:51 or 2:52 after first 
correcting the various terms in these equations by the methods outlined in the foregoing 
sections. 

2.55. Specific Gravity-Strength Relations for Plywood. As in solid wood, the 
strength and elastic properties of plywood increase with an increase in specific gravity. 
The magnitude of this strength increase, however, cannot be determined by the same 
convenient exponential equation given in table 2-1. 



44 



ANC BULLETIN— DESIGN OF "WOOD AIRCRAFT STRUCTURES 



Table 2-8. — Approximate methods jor calculating the strength and stiffness oj plywood 1 



Property 



Direction of stress with respect 
to direction of face grain 



Portion of cross-sectional area 
to be considered 



Allowables expressed as 
proportion of strength values 
given in table 2-3 



Ultimate tensile. 



Ultimate compressive 



Shear 

Shear in plane of plies 



Parallel (Ff UW ) or perpen 
dicular (F tUl ) 

±45° 

Parallel (Fcmu) or perpen 
dicular (F CT , X ) 

±45" {Fcuas") 



Parallel or perpendicular (F^^) 
±45° . .' 



Parallel, perpendicular, or + 45" 



Load in bending. 



Parallel or perpendicular-. 



Deflection in bending 



Parallel or perpendicular 



Deformation in ten- 
sion or compression. 

Bearing at right angles 
to plane of plywood. 



Parallel or perpendicular . 



Parallel plies 2 only 

Full cross-sectional area 

Parallel plies 2 only 

Full cross-sectional area 

Full cross-sectional area 

Full cross-sectional area 

Joints between ribs, spars, etc. 
and continuous stressed ply- 
wood coverings; joints be- 
tween webs (plywood) and 
flanges of I- and box-beams; 
joints between ribs, spars, 
etc., and stressed plywood 
panels when plywood ter- 
minates at joint — use shear 
area over support. 

Bending moment M=KfI/c' 
where I = moment of inertia 
computed on basis of par- 
allel plies only; c' =distance 
from neutral axis to outer 
fiber of outermost ply hav- 
ing its grain in direction of 
span; K = 1.50 for three-ply 
plywood having grain of 
outer plies perpendicular to 
span, if =0.85 for all other 
plywood. 

Deflection may be calculated 
by the usual formulas, tak- 
ing as the moment of inertia 
that of the parallel plies 
plus 1/20 that of the per- 
pendicular plies. (Whenface 
plies are parallel, the calcu- 
lation may be simplified, 
with but little error, by tak- 
ing the moment of inertia as 
that of the parallel plies 
only). 

Parallel plies 2 only 



Loaded area . 



Modulus of rupture. 
One-fourth modulus of rupture. 
Maximum crushing strength or 

fiber stress at proportional 

limit, as required. 
One-third maximum crushing 

strength or one-third fiber 

stress at proportional limit, 

as required. 
1.18 times the shearing strength 

parallel to grain. 
2.35 times theshearing strength 

parallel to grain. 
One-third the shearing strength 

parallel to grain for the 

weakest species. 



Modulus of rupture or fiber 
stress at proportional limit, 
as required. 



Modulus of elasticity. 



Modulus of elasticity. 

Compression perpendicular to 
grain. 



• 1 These simplified strength calculations are to be used only as a rough guide in preliminary design work, and are not 
acceptable for final design when the results obtained differ considerably from those obtained by the more accurate methods 
given in this bulletin. 

2 By "parallel plies" is meant those plies whose grain direction is parallel to the direction of principal stress. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



45 



In the manufacture of plywood, no requirements have been set up to control the 
specific gravity of the individual veneers and consequently there is no assurance that the 
final plywood specific gravity will fall within a certain range. The "weight per square 
foot" column in table 2-9 for various plywood constructions has been based on the 
average specific gravity values for wood listed in table 2-3. 

The strength properties for a piece of plywood are merely the composite strengths 
of each individual veneer in the direction being considered. Therefore, to make a ra- 
tional specific gravity correction to plywood strength test data, it is first necessary to 
determine the specific gravity of each individual veneer and then correct its strength 
properties to correspond to the average specific gravity value given in table 2-3 for that 
species. To do this, of course, is impractical and the problem is further complicated by 
the effect of glue impregnation. 

When substantiating the strength of a plywood structure, or when establishing de- 
sign values from static tests, the weight per square foot of the plywood used in the 
specimens should be near the values given in table 2-9 to minimize the effect of high 
or low specific gravity values. 

2.56. Stress-Strain Relations for Wood and Plywood. When stresses are applied to 
wood or plywood in a direction at an angle to the grain, the resulting strains are quite 
different from those obtained in isotropic materials. Mohr's stress-and-strain circles are 
a means of showing, graphically, the relation of stress or strain in one direction to the stress 




Figure 2-10. — General stress distribution in plywood. 



46 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



or strain in any other direction and are an aid in the visualization and evaluation of these 
relations. Reference 2-25 treats extensively the general problem of the use of Mohr's 
circles in connection with wood and plywood. However, only a limited general treatment 
is presented herein, together with a few specific examples of calculated Mohr's-circle 
constants and of the use of the Mohr's circle in determining the elastic properties of 
45° plywood. 

2.560. Derivation of general stress-strain relations for plywood. In this section 
is presented the general method of analysis that is applicable both to simple stress (either 
direct tension, compression, or shear acting independently) and also to combinations of 
stresses. 

2.5600. Obtaining strains from given stresses. Assume a stress distribution in a 
piece of plywood as shown upon the outer square in figure 2-10 (direction of arrows 
indicates positive direction). The stress circle can be drawn by use of the following 
equations as shown in figure 2-11, and the stresses parallel and perpendicular to the 
face-grain direction can be determined. 



/ 



(2:24) 




R = V (/i-C) 2 +(/ sl ) 2 



(2:25) 




D '*ECTI0H 



NORMAL 
STRESS 



+ 



C 



+ 



Figure 2-11. — Stress circle for stresses shown in figure 2-10. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



47 



The strains parallel and perpendicular to the face-grain direction can be found by 
use of the equations 

— p*. e x =J§ w~V.«, e sw =j^- (2:26) 



Ihw &x & x &w ^(Ju 

where : 

[x wx and y. xw are given by equations 2:22 and 2:23, respectively. 
The strain circle can then be drawn, by the following equations, as shown in figure 
2-12 and the strains in any direction can be determined. 

c=|(e w +ex) (2:27) 



r = V (e w -c) 2 +(e sw y (2:28) 

Thus, curves similar to those in figures 2-16 to 2-19 can be constructed by assuming a 
stress of 1 pound per square inch to be applied at various angles to the face-grain direction 
and solving for the values of c and r for each of these angles. 




Figure 2-12. — Strain circle resulting from equation (2:26). 



48 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



2.5601. Obtaining stresses from given strains. The foregoing process can be re- 
versed if strains are given and stresses required. For this purpose strains are usually- 
measured in the three directions shown in figure 2-13. The strain circle can be drawn, 
by use of the following equations, as shown in figure 2-14, and the strains parallel and 
perpendicular to the face grain can be found. 




Figure 2-13. — Directions of measured strains. 




Figure 2-14. — Strain circle for measured strains. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



49 



c = ^(C'+c^) e,,=e 8 —c r = y/(e, — c)W(e»,.2) (2:29) 

The stresses parallel and perpendicular to the face-grain direction can be obtained 
from the following equations: 

fw-&w j_ ( — — s fx = I!i x , — — fsw = 2G wz e sw (2:30) 

The stress circle can then be drawn, by the use of the following equations, as shown 
in figure 2-15, and the stress at any angle to the face grain direction may be found: 

C=~ (U+fx) (2:31) 



R = V(U-Cy+(f aw )* (2:32) 





/SHEAR STRESS 


\ NORMAL 
ISTRL55 








v — rr~ + 






c 



Figure 2-15. — Stress circle resulting from equations (2:30). 



2.561. Stress-strain relations for specific cases. 

*2.56lO. Stress-and-strain-circle constants. Stress-and-strain-circle constants have 
been calculated for unit stress (1 pound per square inch) for plywood made of four differ- 
ent species and having constructions incorporating various ratios of areas of plies running 
in one direction, to total plywood area. These are plotted in figures 2-16 to 2-19 and 



50 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



have been calculated by use of the elastic constants that were obtained experimentally 
by Jenkin (ref. 2-6) and which are presented in the first four lines of table 2-5. The 
designer may, by the use of the general relations derived in section 2.540 (or in reference 




UNIT OF TENSILE STRESS - ROTARY % • 60'/. UNIT OF TENSILE STRESS- ROTARY £ • SOX 



Figure 2-16. — Strain circle constants for rotary-cut plywood subjected to tension or compression. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



51 



2-25) and elastic-constant data obtained from table 2-5 or section 2.13, calculate the 
stress-and-strain-circle constants applicable to any particular plywood construction. 
Figures 2-16 and 2-17 cover simple tension in the plane of plywood made of rotary- 





Figure 2-17. — Strain circle constants for sliced plywood subjected to tension or compression. 



52 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 





I t M WALNUT 



'0' 10' 20' JO' 40' SO' 60' 70' SO' 90- 

$ 

WIT OF TENSILE AND COMPRESSIVE STRESSES - ROTARY 




C 10' iO' 30' 40' SO' 60" 70' SO' 90" 

6 

UNIT OF TENSILE AND COMPRESSIVE STRESSES - ROTARY £ -SO'/. 




UNIT OF TENSILE AND COMPRESSIVE STRESSES - ROTARY 

Figure 2-18. — Strain circle constants 




V 10' 20' JO' to' SO' 60' 70' so' sor" 



UNIT OF TENSILE AND COMPRESSIVE STRESSES ~ ROTARY 30% 




1* . 1 ■ — — 1 1 1 ! 6 

0' 10' 10' 30 40 SO 60' 70' 60 «T 



S 

UNIT OF TENSILE AND COMPRESSIVE STRESSES - ROTARY yf'lOZ 




10' To' 30' W 60' TO' SO' 30, 



I 

UNIT OF TENSILE AND COMPRESSIVE STRESSES - ROTARY ^ -SOX 

rotary-cut plywood subjected to shear. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



53 





Figure 2-19. — Strain circle constants for sliced plywood subjected to shear. 



54 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



cut and sliced veneers, respectively. Figures 2-18 and 2-19 cover tension in one direction 
and equal compression in a direction 90° to the tension, for plywood made of rotary-cut 
and sliced veneer, respectively. The combined action of these two stresses is equivalent 
to a shear stress equal to the tensile stress and acting at an angle of 45° to it. 

Each curve sheet applies to a group of plywood constructions in which all the plies 
are of the same species and the cross-sectional area of all the plies running in one direction 
is a certain fraction of the total cross-sectional area of the panel. This fraction is denoted 

by upon the individual curve sheets. The curve sheets contain curves for spruce, 

mahogany, ash, and walnut, computed from the elastic constants for these species given 
in the first four lines of table 2-5. When the same curve applies to two different species, 
a line is used denoting one species and the curve labeled with the first letter of the other. 

The curves apply only to the simple stress noted above but they can be combined 
for more complicated stress by the usual method of combining strain circles when an 
isotropic material is considered. 

The curves are not accurate at angles 0° and 90° to the grain, and for these angles, 
the methods given in section 2.6 should be used. In the use of figures 2-16 to 2-19: - 

6 = angle 3 between direction of face grain and the principal axis of tension measured 
positively counterclockwise from the grain direction to the axis. 

<j> = angle 3 between direction of face grain and the principal axis of extension measured 
positively counterclockwise from the grain direction to the axis. 

r = radius of strain circle. 

c = distance between the origin and the center of the strain circle. 

2.5611. Stress-strain relations in plywood at 45° to face grain direction. In 

this section are presented the specific applications of the general stress-strain relations 
given in section 2.560 to plywood loaded at 45° to the face grain. 




J 



f, 



Figure 2-20. — Plywood in tension at 45° to the face grain direction. 



s When becomes less than 50 percent, the same figures may be used provided the angles 6 and <J> are taken 90° to 

A 

the face grain: that is, the plies of predominant thickness should always be considered as the face plies. 



STRENGTH OP WOOD AND PLYWOOD ELEMENTS 



55 



2.56110. Tension at 45° to face grain. This case is shown in figure 2-20. 
Equations (2:24) and (2:25) yield: 

C=gfrfoTf t =0 (2.33) 

R=-f t ioTf tl =0 (2:34) 

From this the stress circle can be drawn, as shown in figure 2-21. 
The circle passes through the origin, since C = R, and : 

t -It t -It t -It (2.35) 

JW~^Jl Jx—qJ1 JSW—^Jt 

Acting parallel to the face grain is/„ and/ SJ ., and/ SU) acts at right angles to these two. 
The strains in these directions can be obtained from equation (2:26). 




Figure 2-21. — Stress circle for plywood in tension at 45° to the face grain direction. 



56 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



From these, the strain circle can be drawn, as shown in figure 2-22. Figure 2-22 is 
not based upon actual quantitative values applicable to any particular plywood con- 
struction, but upon the general assumption that E w >E X (e w <e x ). For this general case, 
the principal axis of strain is not parallel to the direction of the tensile stress. 




SHEAR STRAIN 



Figure 2-22. — Strain circle for plywood in tension at 45° to the face grain direction. 

The modulus of elasticity at 45° to the direction of the face grain is defined as the 
ratio of a tensile (or compressive) stress in this direction to the strain in this direction 
which the stress produces, hence 

4 

(2:37) 



Ea5=—-=- 



Ci 



~E7 



J_ (Aw 



1 

G-wx 



with an associated shear strain 



i=ei Kai (A L) 

A \ E x E w ) 



Values of G wx can be calculated from equation 2:20. Values of y. wx , \x. xw can be calculated 
from equations 2:22 and 2:23 and notes thereunder. 
Where E X = E W (as in balanced construction of one species): 

2E W 



E 1.5—' 



E u 



and e a i —0 



(2:38) 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



57 



i 

In a balanced construction the equation E is =-^r, where c and r are obtained from 

figures 2-16 through 2-19, may also be used to obtain E, if> . 

2.56111. Shear at 45° to the face grain. This case is shown in figure 2-23. Equa- 
tions (2:24) and (2:25) yield: 

C=0 as/, and/ 2 = (2:39) 

ft=/ sl as C and/,=0 (2:40) 

The center of the stress circle is at the origin and can be drawn as shown in figure 2-24. 

This shows that the principal axis of stress is parallel to the grain direction. It also 
shows that 

f w = -fsi f,=f„ f*» = (2:41) 
The resulting strains are obtained from equation (2:26) 

-^bt+ltf) e * =i - (ir+W, e "- =0 (2:42) 



*sz 




fsz 

Figure 2-23. — Plywood in shear at 45° to the face grain direction. 
From equation (2:27) 



58 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



< 




The resulting strain circle is shown in figure 2-25. The value of c is negative and there- 
fore the center of the circle lies to the left of the origin. Since e sw = 0, the direction of e w , 
and therefore the direction of the face grain, is parallel to the direction of the principal 

axis of stress. 

The modulus of rigidity at 45° to the grain direction {G is ) is defined as the shear 
stress divided by the shear deformation, or 

G iS =^-=—. j (2:45) 

We e ~e~ 

The associated direct strain 

For E W = E X , e, =0, and the center of the strain circle coincides with the origin. Then 
which is the relation obtained for isotropic materials. 



I 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



59 




*2.56ll2. Experimental stress-strain data. Figure 2-26 presents stress-strain curves 
typical of those obtained in a few exploratory tests of plywood to which the stresses were 
applied at 45° to the face grain direction and in which the grain direction of alternate 
plies was at 90°. The types of specimen on which these curves were obtained are also 
indicated in figure 2-26. For experimental stress-strain curves, see reference 2-26. 

2.6. PLYWOOD STRUCTURAL ELEMENTS. The following formulas for 
strength of plywood elements are applicable only when elastic instability (buckling) 
is not involved, except in the case of column formulas. For cases involving buckling, 
see section 2.70. 

2.60. Elements (6 = 0° or 90°). 

2.600. Elements in compression (6 = 0° or 90°). When a plywood prism is sub- 
jected to a direct compression load, the relation between the internal stress (/ c l) in any 
longitudinal ply and the average P/A stress is given by the following equations: 

Face grain parallel to applied load 

P/A &) (2:47, 




(Nl OS U3d 97) S-S-JVIS- 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



61 



Face grain perpendicular to applied load 

PM (2:48, 

The allowable stresses at the proportional limit F cpw and F cvx , or the allowable ulti- 
mate stresses F cuw and F eux are obtained from these equations, respectively, when the 
stress at the proportional limit F CP or the ultimate crushing stress F cu from table 2-3, 
whichever is required, is substituted for/ ( L. When more than one species is used in the 
longitudinal plies, the species having the lowest ratio of F,. p /El and F,- u /El must be used 
in determining the correct allowables. For certain species and plywood constructions, 
the compression allowables may be obtained from table 2-9. 

*2.601. Elements in tension (6 = 0° or 90°). Under tension loads the fiber stress 
at proportional limit for wood is, in most cases, very close to its ultimate strength. This 
fact should be given careful consideration in the design of wood and plywood tension 
members, and stress concentrations should be avoided. An equalization of stresses for 
loads above the proportional limit cannot be assumed, as in the case of metal structures, 
since yielding will be closely followed by complete failure. 

The allowable ultimate tensile stress for a plywood strip (designated as F tU w when 
the face grain direction is parallel to the applied load, and F tux when the face grain is 
perpendicular to the applied load) is equal to the sum of the strengths of the longitudinal 
plies divided by the total area of the cross section. The strength of any longitudinal ply 
is equal to its area multiplied by the modulus of rupture for the species of that ply as 
given in column 8 of table 2-3. For certain species and plywood constructions, the ten- 
sion allowables may be obtained from table 2-9. 

*2.602. Elements in shear (0 = 0° or 6 — 90°). The allowable ultimate stress 
F swx of plywood elements subjected to shear is equal to the sum of the shear strengths 
of all plies divided by the total cross-sectional area. The shear strength of any individual 
ply in a direction parallel to that of its grain is the allowable shear stress parallel to the 
grain (column 14 of table 2-3) multiplied by the cross-sectional area of that ply. The 
shear strength of any ply in a direction perpendicular to that of its grain can be taken as 
1.5 times the allowable shear stress parallel to the grain (column 14 of table 2-3) multi- 
plied by the cross-sectional area of that ply. Thus, two allowable shear stresses will be 
obtained, one parallel to the face grain and one perpendicular to the face grain; but since 
shear stresses are always applied equally in these two directions, the lesser value of the 
two is the proper allowable stress to use. The ultimate shear stresses for certain species 
and plywood constructions both parallel and perpendicular to the direction of the face 
grain have been computed. The lesser of the two are given in column 20 of table 2-9. 

A few exploratory tests indicate that the shear values of table 2-9 are applicable 
to plywood made from veneers of approximately V nrinch thickness and that an increase 
in strength may be expected from plywood made of thinner veneers. This effect is being 
further investigated. 

2.61. Elements (6 = any angle). 

*2.6l0. Elements in compression (6 = any angle). Based upon the results of com- 
pression tests of a few species and constructions of plywood, the ultimate compressive 
stress may be given by : 



62 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



F cu6 F cuw qq° cuw Fcux) (2:49) 

where : 

6= angle between the face grain and the direction of the applied load in degrees. 
F cu w = ultimate compressive strength of the plywood parallel to the face grain; from 
formula (2:47) 

Fcux = ultimate compressive strength of the plywood perpendicular to the face grain; 
from formula (2:48). 

*2.6ll. Elements in tension (0 = any angle). The ultimate tensile strength of ply- 
wood in this case is given by the formula: 

F tu9 = — 1 (2 :50) 

rcos 2 6 "1 2 , rsin* 0~i 2 . rsin 6 cos 

where: F tU w and F tux = ultimate tensile strength of plywood parallel and perpendicular" 
to the face grain direction, respectively, from section 2.601; and 

F swx = ultimate shear strength of the plywood when the face grain direction is parallel 
and perpendicular to the shear stresses, from section 2.602. 

*2.6l2. Elements in shear (0 = any angle). The ultimate shear strength of ply- 
wood in this case is given by equations (2:51) and (2:52). When shear tends to place 
the face grain in tension, equation (2:51) should be used. When shear tends to place 
the face grain in compression, equation (2:52) should be used. 

When face grain is in tension 



y 




(2:51) 



- X 



When face grain is in compression 



v 




(2:52) 



For the special case of the face grain at 45° to the side of the panel, equations (2:51) 
and (2:52) reduce to 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



63 




(2:53) 



(2:54) 



*2.613. Elements in combined compression (or tension) and shear (0 = any 
angle). The condition for failure of plywood elements subjected to combined stresses 
in the plane of the plywood is given by the following equation. Formulas 2:50 to 2:54 
are special cases of this general equation. 

^)'+( / t)' + (fe)'-' ■ 

where : 

f w /F u , = ra,t\o of the internal tension or compression stress, parallel to the face 
grain, to the allowable tension or compression stress in the same direction. 

fx/F x = ratio of the internal tension or compression stress, perpendicular to the 
face grain, to the allowable tension or compression stress in the same 
direction. 

fs w x/F s wx — ratio of the internal shear stress, parallel and perpendicular to the face 
grain, to the allowable shear stress in the same direction. 

In the use of equation 2 :55, it is necessary to first resolve the internal stresses into 
directions which are parallel and perpendicular to the face grain direction. 

In order to clarify the use which can be made of the combined loading equation 2:55, 
the complete derivation of equation 2:50 is given. It is desired to find the allowable 
tensile stress of a plywood element which is loaded as shown in figure 2-27. 




Figure 2-27. — Orientation of plywood element for derivation of formula 2:50. 



04 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



Resolving stresses 

ftw=ft cos 2 6 
ft x =ft sin 2 
fsw X =ft sin cos 6 
Substituting these terms in the combined loading equation 

the following is obtained: 

Vft cos 1 6 1* | V f t sin 2 8 V | V f t sin cos ~|~ 1 
L P'tuw J [_ Ftux J |_ F IWX J 

Dividing through by /, and setting its value equal to the allowable tensile stress, F tu e, 
gives equation 2:50, or 

F tu9 = (2:50) 



4 



cos 2 6 1 2 p sin 2 6 "| * r sin cos 6 -| 8 



Equations 2:51 and 2:52 may be derived in exactly the same manner. Experiments 
indicate that equation 2:55 is conservative in the case of compression at angles to the 
grain and that equation 2 :49 can be used. 

2.614. Elements in bending. The apparent moduli of elasticity {E fw and E fI ) of 
plywood beams in bending are given by the general formulas in section 2.5. When all 
of the plies are of equal thickness and one species, these general formulas reduce to the 
following forms : 
For rotary-cut veneer, 

3-ply;^=|(|+^) **HsK 1+ "s9 (2:56) 

5-ply; 2^=J§ (^+99) Z^=J§ (»+"f=) (2:57) 



7-ply; E fw =^ (99 f+m) E fx =^ (90+144 f) (2:58. 

9-ply: E fu -^ (®44 %+^ 85 ) EfI= W9 { 2 ^ + ^ 85 ( 2:59) 

For quarter-sliced veneer, Et/El should be replaced by Er/El (sec. 2.13). 

The bending stress in the extreme fiber of the outermost longitudinal ply is given by 
the following formulas: 

Face grain parallel to span 

'^mi (B (2:60) 

Face grain perpendicular to span 

^ = 7^r(lt) cfor3 - ply) • (2:61) 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



65 



'»=^(j7> Uother) (2:62) 



Mc' /El 
where : 

c'= distance from neutral axis to extreme fiber of outermost longitudinal ply. 
£" /x = same as E fx except that outermost ply in tension is neglected. E fx may be 

used in place of E' fx in formula (2:62) with only slight error. 
El is taken for the species of the outermost longitudinal ply. 

The allowable bending stress at proportional limit (Fi,„) and the modulus of rupture 
in bending {F bu ) are given in table 2-3. 

**2.6140. Deflections. The deflection of plywood beams with face grain parallel or 
perpendicular to the span may be obtained by using E fw or E fx in the ordinary beam 
formulas. E' fx is used only for determining strengths in bending and not the deflection. 
For plywood beams with face grain at an angle 6 to the direction of the span, the effective 
modulus of elasticity to be used in the deflection formula is given by the equation : 

E = E fw cos*Q+-£ sin 2 6 cos 2 V+E, x sin* 6 (2:63) 

o 

when 

(1) The loading is constant across the width of the beam at any point in its span. 

(2) The beam width is sufficient to cause the. deflection to be constant across the 
beam at any point in the span. 

(3) The beam is held so that it cannot leave the supports. 

There are no methods available by which the bending stresses in plywood beams 
may be calculated when the grain direction of the face plies is other than parallel or per- 
pendicular to the span. (ref. 2-24.) 

*2.6l5. Elements as columns. The allowable stresses for plywood columns are 
given by the following formulas: 

Long' columns 

■p^_ 0.85 ir Eju, ££ ace g ram p ara ll P l to length) (2:64) 



0.85 7T * E 



fx 



(face grain perpendicular to length) (2:65) 



(L'/ 9 ) cr =3,55yJ E 



F c u w 

or 3.55 yjy^- respectively 



Short columns 



'-'-['-i (2:66) 



where : 

K = (L'/ P ) cr 

Fcu — Fcuw when face grain is parallel to length. 

= F CUX when face grain is perpendicular to length. 



66 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



OS A £3 

a m s 



3 1 



3 1 



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5 S ° e5 3 S 5 S 



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STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



67 



2,820 
3,080 
2,700 
2,350 
2,710 
2,460 
3,190 


3,520 
2,920 
3,070 
2,750 
2,260 
2,610 
2,440 
3,210 


3,420 
2.900 
3,0?0 
2,720 
2,260 
2,540 
2,400 
3,170 


2,120 
2,700 
2,140 
2,110 

2,190 
2,040 
2,870 


3,300 
2,400 
2,940 
2,360 
2,260 
2,440 
2,280 
3,100 


3,420 
2,510 
3,020 
2,400 
2,200 
2,540 
2,380 
3,170 


1,430 
1,160 
1,130 
1,110 
1,500 
1,300 
1,100 


1,810 
1,420 
1,200 
1,160 
1,140 
1,540 
1,300 
1,140 


1.S40 
1,420 
1,210 
1,170 
1.140 
1,500 
1.310 
1,150 


! ! I § ! § ! 


7,270 
4,270 
5,440 
4,270 
4,550 
5,440 
4,270 
5,390 


§ ! III! ! S 


9,300 
6,960 
6,960 
5,100 
6,960 
6,960 
6,900 


8,230 
8,230 
6,160 
6,160 
4,550 
6,160 
6.160 
6,110 


3 S I I S I I s 


2,180 
2,930 
2,250 
2,320 
2.310 
2,130 
3,160 


3,600 
2,510 
3,340 
2,560 
2,610 
2,660 
2,400 
3,600 


3,810 
2,650 
3,530 
2,710 
2,610 
2,820 
2,610 
3,800 


4,480 
4,120 
4,020 
2,900 
3,340 
3,340 
4,440 


4,030 
3,990 
3,710 
3,590 
2,610 
2,980 
2,980 
4,000 


3,810 
3,770 
3,530 
3,401) 
2,610 
2,820 
2,820 
3,800 


1,640 
2,200 
1,690 
1,740 
1,730 
1,600 
2,530 


2,700 
1,880 
2,510 
1,920 
1,960 

1,850 

2,880 


2,860 
1,990 
2,650 
2,030 
1,960 
2,120 
1,900 
3,040 


3,360 
3,090 
3,020 
2,180 
2,500 
2,500 
3,550 


3,030 
3,000 
2,790 
2,700 
1,960 
2,240 
2,240 
3,200 


2,860 
2,830 
2,650 
2,550 
1,900 
2,120 
2,120 
3,040 


g i § 1. I- § -3 


i g a g s § • i i 


1,020 
759 
752 
774 
747 
741 
747 

1,010 


1,200 
879 
857 
830 
877 
877 

1,190 


1,080 
1,070 
792 
766 
747 
784 
784 
1,070 

1,020 
1,010 
752 
725 
747 
741 
742 
1.010 


3 641 

5 053 

3 929 
3.860 

4 331 

3.393 
5.009 


11.307 

6 951 
9 397 

7 325 

7 340 

8 402 
0.032 
9.310 

19.224 

11 726 
15.704 

12 254 
11 287 
14.387 
11.277 
15 569 


20 60 
15.47 
15 43 
11 85 
15 43 
15 43 
15 34 


30 94 

30 89 
23 26 
23,16 
17.74 
23 15 
23 15 
23.06 


40 46 
46 38 
34.97 
34 78 
27 27 
34 77 
34 77 
34 00 


§ g | | 8 § 1 II I ! § 1 6 § I 


11 783 
7 731 

11.913 
8.080 
7 442 
9 302 
7 430 

10,830 


12.63 
11 .74 
11 ,71 

7.81 

9.98 
9.98 
10.67 

18.96 
18 93 
17 64 
17.57 
11 70 
14 97 
14.97 
16.04 


28 47 
28.42 
26 53 
26.38 
17.98 
22 48 
22 48 
24 1 1 


S 2 « « = 5 B ISSSgiss I S 3 2 S ' 3 £ 3 g 


158 1 

181 

183 

164 

137 

138 

244 

255 
206 
226 
230 
214 
185 
186 
305 


3BS83SS8. 


1,670 
1,190 
1,180 
1,190 
1,210 
1,210 
1,600 


1,600 
1,600 
1,140 
1,140 
1,140 
1,160 
1,100 
1,540 


1,570 
1.500 
1,120 
1,110 
1,140 
1,140 
1,140 
1,510 


.338 

.308 

.288' 

.275 ' 

.308 

.288 

.308 


.494 
.414 

.388 
.358 
.342 
.388 
.358 
.388 


.012 
.505 
.478 
.438 
.398 
.478 
.438 
.478 



illlllllilllH 


S1IIIII1 


IISlSlsl 


Ilililllliilllli 


CO 03 03 03 CO 03 03 


03 03 CO 03 


CQ CQ CQ CQ 


03 03 03 O3O3 03 03CQ 


Diren-yeiiowpopiar 

Mahogany-mahogany 

Mahogany-yellowpoplar 

Yellowpoplar-yellowpoplar 

Sweetgum-sweetgum 

Douglas-fir-Douglas-fir 


Birch-birch 

Birch-yellowpoplar 

Mahogany-yellowpoplar 

Yellowpoplar-yellowpoplar 

Douglas-fir-Douglas-fir 


Birch-birch 

Birch-yellowpoplar 

Mahoganv-mahogany 

Mahogany-yellowpoplar 


li 


.100 
.100 
.100 
.100 
.100 
.100 
.100 


.125 
.125 
.125 
.125 


s g § | 





STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



69 



3.090 
2,330 




1 

Cl 


1 

Cl 


§ 

co 


i 

CO 


1 

IN 


1 

CO 




I 

Ol 




1 

Ol 


CO 


2,810 
2.190 


1 

<M 


2 
oi 


| 

Ol 


I 

Ol 


i 

CO 


1 


i 
Ol 


I 

0-1 


1 

Ol 


2 
■°. 

Ol 


1 

Ol 


I 

CO 


1,180 
1.130 


S 

l-H 


1 


1 




1 


i. 


s 


§ 




§ 


s 


s 


! I 


1 

CO 


I 


i 

CO 


1 


S 


I 


1 


I 


1 

-r 


1. 


i 


1 

uo 


6,610 
6,130 


1 


O 
S . 


§ 


I 


1 


I 
SO 


f 


1 


2 


1 


§ 




3,110 
2,350 


1 

CI 


s 

ci 


1 


I 

CO 


§ 

co" 


1 

Cl 


1 

CO' 


1 

C-l 


| 
Ol 


g 

Ol 


"i 

Ol 


R 

co" 


3,940 
2,890 


! 

<M 


1 

CO 


| 

CI 


1 

-*< 


1 

CO 


I 

CO 


1 

CO 


1 

Cl 


1? 

cq" 


1 

Ol 


1 

of 


I 

CO 


2,340 
1,760 


O 

72 


I 




j 

OJ 




O 


1 

Cl 


i 


1 


I 

Cl 


1 


1 

Ol 


2,960 
2,160 


o 

Cl 


I 


1- 

Ol 


1 

CO 


I 


g 
». 


! 

d 




1 

CM 


1 

Cl 


1 

Ol 




I £ 


i 


s 


§ 


1 




K 


g 










i 


1 1 




1 


i 


5 


1 


1 


g 




s 






I 


18.2 
14.2 






2 




o 


CO 


OS 


Si 




s 


s 


s 


a s 






S3 




g 
















13.83 
9,39 


8 


«. 


o 


s 

2 


s 

SJ 




S 




s 




3 


ol 

2 




2 


s 


S 


S3 


c§ 




S 


S3 


Si 






o 

CO 


S 1 




1 






1 


I 




I 




I 




1 


S 1 


I 


S 


I 


§ 


s 


5 


2 




I 


I 




i 


1 1 




! 


i 


s 


s 


2 

3 


1 




I 


1 


1 


s 




2 






i 




1 


1 


§ 




s 


s 


1 




« PP 
fa fa 


pq 

fa 


pq 

fa 




PQ 


PQ 

fa 


pq 
fa 


pa 

fa 


PQ 
fa 


pq 


pq 
fa 


pq 
fa 


pq 

o =a £2 o 

fa 



70 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



jl 



I 1 I 
I I- I 

I 1 S 



8 I 
3 S 



.5 

f'l 



5 



S ! 



3 



! ! § !■ I 1 



I 



f! 



I ! 



§ I ! 1 



I ! 



I I S 



! ! i 



11 



Hi 




All 



i 



I- 1 1 § I g I i 



si 



iiiiiiiiiiiiiisiiiiiiiii 



i-Q CQ CQ CQ CQ CQ CQ CQ 



1 



§ § s a s i § 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 71 



3,520 
2,670 


! 


! I 


I 


1 


! 


S3 


1 




! 


! 


1 


! 


s 
3 


3,310 
2,320 


1 


2,290 


1 


1 


s 


s 

S3 


1 




! 


1 


1 


! 


1 


1,820 
1,320 


! 




§ 


s 




| 


s 


2 


2 

3 


1 




1 


1 


!- 


7,320 
4,180 


i 


4,180 
4,180 


1 

■a 


§ 


1 


B 




I 


« 


i 


! 


i 


2 

lO 


8,180 
7,220 


§ 


5,820 
4,920 


1 

CD 


s 


§ 


B 


1 


! 


I 


! 


1 


! 


2 
ui 


3,620 
2,450 


s 


2,490 
2,420 


1 


8 

cxf 


1 


o 

s 


1 


I 


! 


I 


1 


! 


! 


4,010 
3,470 


i 


2,750 
2,800 


1 


g 

M 


1 


c 

s 


1 


I 


2 
5 


1 


I 


I 


? 


2,720 
1,840 


i 


1,870 
1,820 


o 


O 

3 


1 


I 


1 


I 


1 


| 


s 


! 


1 


3,010 
2,600 




2,060 
2,100 


i 


1 


§ 
si 


1 


o 

3 


I 


1 


i 


s 


S 


I 


s i 




5 1 


£ 


1 


S 


1 


a 


E 


2 




a 


« 


1 


| i 


s 


I 1 


g 


g 


s 


! 


I 




a 


1 


a 




§ 






S S3 








s 


s 




ss 


sg 


g- 


s 




105.0 
103.0 


to 

e 


77.6 
60.9 


s 


CD 


g 


2 


I 


=, 

s 


3 


5 


CO 


o 


s 


36.47 

23.88 


si 


24,31 
23 53 


s 


S3 


2 


s 
s 


s 

S3 






S 

S3 


2 


s 

S3 


9 
S 


s s 


s 


S? S 


s 


g 




s 


s 




3 


s 


3 


s 


a 


1 1 


1 


s 1 


1 


I 




1 


1 




I 


I 


I 


1 


1 


1 1 


1 


5 g 


1 




§ 




I 


I 


1 


1 


I 


I 


s 


1 i 


1 


1 1 


§ 


g 


s 




s 


1 


1 


1 


1 


1 


s 


0.981 
.784 


g 


I 1 


g 


i 


g 


1 




§ 




1 


s 




§ 


. |llll|l.|ll|ISi-|SilllS||l|l§l! 


fllilillilllllll 


Sill 


&. &. 


m 
fa 


PQ PQ 

&, fa 


m 
fa 


eq 

fa 


fa 


CO 

fa 


pa 

< 
fa 


CQ 

fa 


fa 




m 

fa 


CQ 

fa 


CQ 
fa 


Birch-yellowpoplar 


1 


- 

i 

i 


Yellowpoplar-yellowpoplar 






| 


Birch-birch 


Birch-yellowpoplar 


) 


Mahogany-yellowpoplar ' 


Yellowpoplar-yellowpoplar 


| 


Sweetgum-yellow poplar 




1 1 


S 




I 




1 


=* 




2 


2 

"5 


2 

<™ 


2 

» 


2 


2 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 





! \§\sri 


3,470 
2,620 
3,040 
2,200 
2,290 
2,570 
2,280 
3,190 


1! 


i 


I 






3,370 
2,400 
2,980 
2,350 
2,240 
2,500 
2,310 
3,150 




1 


I 




1,830 
1,300 
1,210 
1,150 
1,130 
1,550 
1,240 
1,140 


Ultimate 
strength in 


1 


1 






8 § § 


' S § 1 - i 1 

-r' .re" ■#" « 


1 






I 1 I -S 8 i J 1 

.re .c r» .re" .re .re' 






crushing 
strength 


s 

hi 






3,720 
2,580 
3,450 
2,010 
2,550 
2,760 
2,550 
3,720 


1 


3" 


as If 


1 1 1 1 1 I 

sf M CO' N of 5, 


! I S 


Fiber stress at! 


proportional 
1 imit 








2,800 
1.930 
2,590 
1,960 
1,910 
2,070 
1,910 
2,970 


I 






2,930 
2,430 
2,700 
1,970 
2,010 
2,170 


? 1 


"3 

J 




a 




1 M 




a 
65 






1.050 
927 
768 
751 
765 
759 
761 

1,040 


Static bending 


Moment for 


modulus of 
rupture 


ill 

S: 




Mi 


157.5 
93.4 

121.0 
94.6 
92.5 

117.9 
92.4 

120.0 


"i — 
& - 


o 


I n.-lb. 

per 
in. of 
width 


213.5 
211.6 
162.8 
159.U 
125.3 
159.8 
159.8 
161.4 


ii 




111 




In.-lb. 

per 
in. of 

width 


i 1 I 1 i 111 


iir 


1» 


g 


In.-lb! 

per 
in, of 
width 


130.8 
129.7 
123.5 
121.3 
82.6 
103.3 
103.3 
112.2 


i 


8 


s 


m 


■f. i • i i , i i i N i 






■a 

&? 


§ 


1 &-s 


1 S.I II 11. s 


3 






1 M 


| | 1 S I ' S " 8 I 


I 


m 


(15 
per- 

mois- 
ture) 2 






1,480 
1.120 
1.155 
1.020 
.900 
1.155 
1.020 
1.155 


si 


s 




1 1 1 1 1 i i i i i I i 1 1 § i I i i I i 1 1 i 








«;E23pa=Qqa«« 


1 

'o 

a 

w 
























Nom- 
inal 

thick- 
ness 


— si 
>— < 


.375 
.375 
.375 
.375 
.375 
.375 
.375 
.375 



« 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



73 



mum 



2§2g|gg| 

3 «■ £- «• S- s s s 



SSS999S9 



Ill-Ill!! 



IHISIH 



SSI I 



11111115 



N rH O) rH « 



II: 



399 



ii 

ci CO 



IlliiiSl 



•4 ^ 



ooH«o;iflo:o 



CO of cm' of of « N of 



59393999 



99599999 



ii 



3 S 3393 5 



99555959 



SillllSi 



N - c^" J _J rH I 



II 



Ills! 

of of of Of CO' 



iiiiiisi 



n « n o o a x 

IBsrlSsss 



SISolsllS 



SSIlBlSi 



of of of of of of S 3 ol S" of of of of co' 



rH -h" rH rH rH* rn' rH rH rH -" rH - rH rH rH rH rH _ 



II!I!!!I ISBSSSSi 



I- 1 1 1 ill: 



lisllll 



55595151 51999991 



Slilllll IllllSiS 



leSSIIKS StSMISS 

Of rH Of rH' rH" rH rH of of of of -' - -h' rH - of 



III955I5 



i-SHSUl 



1 1 ! * i 1 1 s 

rH' rH' rH rH rH r-i rH rH 



OOOOOggO 

3 S S I 3 5 5 3 



2 S? § 2 

o * "f o 
00 CD CD 10 < 



IIS 



co of co" of of of of co" 



!!!!!-§!! 



Of of rn" rH- ,H rH of 



iiiiiiii 



rH" rH" 



missis 



1 



SSssISirl 



5SS33533 



pilllll 



2 533 HIS 



ggtsmg 



&H 

I 



3SSS3SS9 



11111111 lilliili 




11111111 



co of of of of of of co" 



ISIS 5 111 



lllllglr! 

r-' 



I i g 1 1 g S I 



3S335332 



llllllil 




lilliili 



74 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



I 
1 

s 

Oh 

I 

a 

&3 



Ultimate 
strength in 
shear 


! 


1 


st{ !!III!!S|I!1!SI!§ 


i 




per 
sg. in. 

3,230 
2,510 
2,900 
2,190 
2,160 
2,400 
2,190 
3,060 


3,230 
2,510 
2,900 
2,190 
2,160 
2,400 
2,190 
3,060 


i 


1 


Lb. 

per 
sq. in, 

1,800 
1,370 
1,190 
1,140 
1,120 
1,530 
1,270 
1,130 


1,800 
1,370 
1,190 
1,140 
1,120 
1,530 
1,270 
1,130 


Ultimate 
strength in 
tension 


i 


OS 


Lb. 

per 
sq. in. 

7,050 
5,300 
5,270 
4,590 
4,140 
5,270 
4,590 
5,230 


§§§§!-!-! 


9 


I 


00 


Lb. 

per 
sq. in. 

8,450 
6,130 
6,330 
5,420 
4,950 
6,330 
5,420 
6,270 


ISSSI-ilS 


]1 


strength 


i 




Lb. 

per 
sq. in. 

3,500 


2,750 
3,260 
2,400 
2,400 
2,590 
2,390 
3,510 


8S|||||2 

m <n" m* n" « «" 3 m 


1 


so 


Lb. 

per 
sq. in. 

4,130 
3,180 
3,800 
2,840 
2,830 


Ill 


4,130 
3,180 
3,800 
2,840 
2,830 
3,060 
2,820 
4,090 


Compression 
Fiber stress at 


.1 


1 
&, 




Lb. 

per 
sq. in. 

2,630 
2,060 
2,440 
1,800 
1,800 


1,790 
2,810 


2,630 
2,060 
2,440 


1,800 
1,800 


1,940 
1,790 
2,810 


1 

&. 


s 


Lb. 

per 
sq. in. 

3,100 
2,390 
2,850 
2,130 
2,120 
2,290 
2,120 
3,270 


3,100 
2,390 
2,850 
2,130 
2,120 
2,290 
2,120 
3,270 


Modulus of 






CO 




IglllllS 






1,000 
lb. per 
sq. in. 

1,110 
910 
810 
811 

809 
803 
807 
1,090 


1,110 

910 
810 
811 
809 
803 
807 
1,090 


Moment for 
modulus of 
rupture 


it* 


s 


In.-lb. 

per 
in. of 
width 

779 
732 
604 
596 
457 
583 
584 
598 


§§133813 


Paral- 
lel 3 


o 


In.-lb. 
per 
in. of 
width 

1,030 
955 
791 
795 
607 
774 
776 
785 


1,460 
1,350 
1,120 
1,120 
857 
1,090 
1,100 
1,110 


;ic bending 

Moment for 
fiber stress at 


[l 




e 






h 




In.-lb. 

per 
in. of 
width 

634 
585 
600 
603 
400 
501 
502 
546 


§S3§§SS£ 


i 

5 


5 
j 




8 


IJi siiiiiis 


SUSHIS 


& 


CO 










1,000 
lb. per 
sq. in. 

1,160 
1,070 
840 
844 
848 
841 
843 
1,130 


§§133333 








3.96 
3.07 
3.09 
2.75 
2.56 
3.09 
2.75 
3.09 


j] 


CO 


= © 


iliiiii 




















s 


s 




Birch-yellowpoplar 

Mahogany-mahogany 

Mahogany-yellowpoplar 

Yellowpoplar-yellowpoplar 


sweetgum-sweetgum 

Sweetgum-vellowpoplar 

Douglas-fir-Douglas-fir 


Birch-birch 


Birch-yellowpoplar 

Mahogany-mahogany 


Mahogany-yellowpoplar 

Yellowpoplar-yellowpoplar 


feweetgum-sweetgum 

Sweetgum-yellowpoplar 


1 


Nom- 
inal 

thick- 
ness 




4 pill!!! 


2222222S 

SSS2SSSS 



11 

if 



1 



11 I 



lit 



1 



llli 

'Sjj.3 

' CM ^ 8-2 



111 
I ill 
Ir 



Willi 



| 2 
J2 o 
o d : 

3 •s 

If 



t! 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



75 



Table 2-10. — Budding constants for plywood 1 
THREE-PLY 





Shear 


Compression 


Face grain 
angle 










45° 




0° 








0° 


90° 


Face grain in 
tension 


Face grain in 
compression 


0° 


and 
90° 


90° 


45° 


Nominal 
thickness 




b'/a 


00 


b'/a 


CK.) oo 


b'/a 


(*.) oo 


b' /a 


b'/a 




b'/a 


(#c) 00 


b'/a 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 


(10) 


(id 


(12) 


(13) 


(14) 


Inch 

0.035 
.070 
.100 
.125 
.155 
.185 


60 

.80 
.75 
.88 
.94 
.95 


2.13 
1.79 
1.85 
1.70 
1.65 
1 .64 


2.05 
2. 11 
2 10 
2 13 
2.14 
2.14 


0.60 
.68 
.66 
.71 
.72 
.73 


. 57 
.78 
.73 
.87 

.93 
.94 


0.95 
1.06 
1 03 
1 10 
1 12 
1 13 


3.50 
3.34 
3.38 
3 27 
3 22 
3 22 


1 74 
1.72 
1.72 
1 71 
1.70 
1.70 


1 88 
1 62 
1 67 
1.55 
1 50 
1 50 


6.71 
.82 
.80 
.87 
.89 
.90 


0.53 
.62 
.60 
.65 
.67 
.68 


0.86 
1 08 
1.03 
1 17 
1.23 
1.24 


84 
.91 
.90 
.93 
.94 
.94 



FIVE-PLY 



160 


1 


25 


1 


42 


2 


13 


.83 


1 


29 


1 


26 


2 


91 


1 


66 


1 


31 


1 


02 


.77 


1 


49 


.97 


190 


1 


35 


1 


36 


2 


12 


.87 


1 


41 


1 


30 


2 


81 


1 


64 


1 


26 


1 


04 


.80 


1 


56 


.98 


225 


1 


37 


1 


35 


2 


11 


.88 


1 


43 


1 


31 


2 


79 


1 


63 


1 


25 


1 


05 


.81 


1 


57 


.98 


250 


1 


30 


1 


38 


2 


12 


.85 


1 


35 


1 


28 


2 


86 


1 


64 


1 


28 


1 


04 


.79 


1 


53 


.98 


315 


1 


29 


1 


39 


2 


12 


.85 


1 


34 


1 


28 


2 


.87 


1 


65 


1 


29 


1 


03 


.78 


1 


52 


.98 


375 


1 


48 


1 


28 


2 


08 


.92 


1 


57 


1 


36 


2 


66 


1 


60 


1 


19 


1 


.08 


.84 


1 


64 


.99 



SEVEN-PLY (All plies oj equal thickness) 

Any I 1.40 | 1.32 | 2.10 \ .89 I 1.46 I 1.32 I 2.75 I 1.62 I 1.23 

NINE-PLY (All plies oj equal thickness) 
Any | 1.52 | 1.26 | 2.06 | .94 | 1.63 | 1.37 | 2.60 | 1.59 I 1.17 

ELEVEN-PLY (All plies of equal thickness) 

Any | 1.59 I 1.22 | 2.03 | .96 | 1.72 | 1.40 I 2.52 I 1.58 I 1.14 | 1.10 



1.06 



1.09 



1.59 



.86 I i.e 



1.70 



.99 



.99 



1 The buckling constants listed in this table correspond only to the plywood thicknesses and constructions listed in table 
2-9 that correspond to Army-Navy specification AN-NN-P-51 lb, (Plywood and Veneer; Aircraft Flat Panel). The values in 

this table were computed as follows: For each construction given in table 2-9 a value of — — was computed from col- 

Ef„. +Ef* 

umns 5 and 6 of table 2-9. These values for each thickness were averaged and the average values were used in entering figures 
2-37, 2-38, 2-39, and 2-40, from which the values of this table were obtained. For a more exact determination of these buckling 
constants or to determine the buckling constants of a plywood construction different from those specified in AN-NN-P-51 lb, 
see section 2.701. 



76 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



2.7. FLAT RECTANGULAR PLYWOOD PANELS. 

2.70. Buckling Criteria. 

2.71. General. When buckling occurs in plywood panels at loads less than the 
required design loads, the resulting redistribution of stresses must be considered in the 
analysis of the structure. The buckling criteria in this section are based on mathematical 
analyses and are confirmed by experiments for stresses below the proportional limit. 
Visible buckling may occur at lower stresses than those indicated by these criteria, due 
to the imperfections and eccentric loadings which usually exist in structures. Experi- 
ments have indicated, however, that the redistribution of stresses due to buckling corre- 
sponds more closely to the degree of buckling indicated by these theoretical criteria than 
it does to visible buckling. These criteria can, therefore, be used in various parameters 
for plotting test results or design allowables against the degree of buckling, and to com- 
pute the degree of buckling in a structure. This is done in sections 2.72 and 2.760. 

Since the mathematical analyses are based on the assumption of elastic behavior, 
these criteria cannot be directly applied when the stresses are above proportional limit. 
The behavior at such stresses has been investigated experimentally for some cases, as 
described in sections 2.72 and 2.760. 

*2.710. Compression or shear. The critical buckling stress of flat rectangular ply- 
wood panels subjected to either uniform compression or uniform shear stresses is given 
by the following general formulas. 



El is for the species of the face plies, from table 2-3. 

K c and K s are factors depending on the type of loading, the dimensions of the panel, 
the edge-fixity conditions, and Poisson's ratio. K c and K s are determined by the following 
methods. 

Let a be the width of a rectangular panel of infinite length of which a portion of 
finite length b is being considered. 

The mathematical treatment of buckling constants presented in this section has been 
based on the assumption that the compression load is always placed on the edge having 
dimension o. In a panel loaded only in shear a dimension of either edge may be taken 




(2:67) 




(2:68) 



where : 



STRENGTH OF N OOD AND PLYWOOD ELEMENTS 



77 



as a, and the panel shall be considered as a p = 0° ease when the face grain is perpendicular 
to the edge having dimension a and as a £=90 o case when the face grain is parallel to 
the edge having dimension a. (Fig. 2-28.) 




/3=0° 

Figi re 2-28. — In panels loaded in shear, a may be a dimension of either edge. For (J = 0°, face grain is 
perpendicular to a; for (i = 90°, face grain is parallel to a. 



One method of obtaining A' s or K c is by the use of figures 2-29 to 2-34 as explained 

in section 2.711. Approximate values of A s or K c suitable for ordinary purposes may be 

obtained by correcting A s00 or K cO0 values in table 2-10 for panel size by means of 

b' b 
figures 2-35 or 2-36. In using these figures — is first obtained from table 2-10 and 

i ; b' 

computed. For a more exact determination of A s or K c or to determine these buckling 

constants for a plywood construction different from those specified in AN-NN-P-511b 

or figures 2-29 to 2-34, calculate — — in accordance with section 2.52, read K s0 r 

or A (00 and b'/a from figures 2-37 to 2-40 and correct for panel size by means of figure 
2 35 or 2-36. 

**2.711. Combined compression (or tension) and shear. Panel edges simply 
supported. The analytical method of determining the critical buckling stresses for 
rectangular panels subjected to combined loadings is quite complicated, and only the 
graphical solutions for a few types of plywood construction are given in figures 2-29 
to 2-34. 

When the plywood construction being used is not the same as any of those illustrated, 
its buckling constants may be obtained by a straight line interpolation (or extrapolation), 
E fw 

on the basis of — — — — , of the buckling constants for two plywood constructions whose 
E 

values of the ratio ^— are fairly close to that of the plywood under consideration. 

V TP 

&fw+&fx 

The values of these ratios for the plywood constructions considered in figures 2-29 to 
2-34 may be calculated with sufficient accuracy by assuming Ay = 0.05 El- 

These figures apply to panels of infinite length and values of the buckling constants 
from the curves must be corrected for actual panel length. Values of the shear constant 



78 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



iv s oo and the compression constant K cX are indicated on the vertical and horizontal 
axes, respectively. The points at which the curve crosses these axes give the values of 
A%oo or /Ceo at which buckling will just occur in a panel of infinite length in either pure 
shear or pure compression. The particular combination of stresses represented by each 
of the four quadrants is shown by the small stress sketches. Buckling will occur under 
these combined stresses whenever the location of a point K s(Xl , K c0 o, lies on or outside 
the curve. 

The curve marked b'/a is the ratio of half the wave length (b') of a buckle in an 
infinitely long panel to its width (a). This ratio is to be used in conjunction with figures 
2-35 to 2-40 in obtaining the correction factors for panels of finite length to be applied 
to K s0 o. 

The curves in figures 2-29 to 2 34 marked y give the slope of the panel wrinkles with 

respect to the O-X axis indicated on the stress sketches. 

The procedure in the use of these figures is as follows: 

(1) From the analysis the shear stress (f s ) and the compression (/<.) or tension stress 
( — fc) acting on a particular plywood panel will have been calculated. 

(2) Determine the ratio f s /f c and, on the figure giving the same plywood construc- 
tion and angle £}, draw a line through the origin having a slope (positive or negative) 
equal to this ratio. When the plywood construction is not the same as that given in the 
figures, this procedure for determining the buckling constant will have to be run through 
on the two most similar constructions and an interpolation of the results made on the 

basis of — — ^ — : 
E fuj+Efx 

(3) The point at which the constructed line crosses the curve gives the critical 
buckling constants K sX and K cOD at which an infinitely long panel will just buckle when 
subjected to the same ratio of shear to compression that exists on the panel in question. 

(4) Read the value of b'/a for the point on the b'/a curve which is obtained by 
projecting horizontally from A' s0 o determined in step (3). 

(5) From the panel dimensions compute b' and b/b'. 

(6) Figures 2-35 to 2-40 will give the ratio of K s /K sX from which the value of 
K s can be computed (A' s is always taken as positive). 

(7) The critical buckling shear stress (F Scr ) may then be determined by equation 
2:68. This represents the maximum allowable shear stress which the panel in question 
can sustain without buckling when subjected simultaneously to a compressive stress 
equal to that given in step (1). 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



79 





-4 



SCALE fOR % AND T 



SCALC FOR % ItID 7 



(c) (J I 

?-PLY(ll)Q-- 30' 2-P L Y (1:1) 45' 

Figure 2-29. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. £1 = angle between lace grain and direction of applied stress. 

Two-ply construction. 



80 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 




(tj If) 

Figure 2-29. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
(combined loading. Edges simply supported. (3 = angle between face grain and direction of applied stress. 

Two-ply construction, (continued) 




fa] (b) 
3-PL1 (I N)Q-0~ 3-PLY (l l l)/3* >i' 

Figure 2-30. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. (i = angle between face grain and direction of applied stress. 

Three-ply construction. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



81 




Figure 2-30. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported, = angle between face grain and direction of applied stress. 

Three-ply construction, (continued) 



82 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




Figure 2-30. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported, p = angle between face grain and direction of applied stress. 

Three-ply construction, (continued) 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 83 




(kl Inn) 
3-PLY (l*:l)/3-45' 3-PLY (l:2:i)/S=0" 




-I I, i 
SCALE FOB % OHO y 

















































-3 






















































r i|\ 






f 






















" 






~ . ■ 


-X 
















0- 


-X 
— 1 


























































-5 

s 


I, 


4 










y 

































' 1 












0- 




























—i 








































- -3 








































































— 4 


























--S 


































iCAlC FOI>%AKD~r 























(n) (PI 

3-PLY (l:Z i)/3- 75- 3-PLY (lit) W 

Figure 2-30. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. (3 = angle between face grain and direction of applied stress. 

Three-ply construction, (continued) 



84 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




(a) 
3-ply(i z i)b- o- 



(b) 

















































— 3 






























































































A 2 
s 




































\ 
















Oi 


- 


f 


























Milk 
1 1 






























Y 













<M- 
















































o i 
V 




1 










/ 


T 




















































— z 






/ 
























l 












s 














3 


V- 


















































































































— i 














-tOll 
JCAL £ FOR % AHO 7 y 





















Figure 2-31. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading with edges clamped. @ = angle between face grain and direction of applied stress. 

Three-ply construction. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



85 




Figure 2-31. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading with edges clamped. £ = angle between face grain and direction of applied stress. 

Five-ply construction, (continued) 



86 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




(C) (ct) 
5-PLY (l:N:l:l)a-30 w 5-PLY (MWOMST 

Figure 2-32.— Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. = angle between face grain and direction of applied stress. 

Five-ply construction. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



87 




Figure 2-32. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. £ = angle between face grain and direction of applied stress. 

Five-ply construction, (continued) 



88 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 





(k) cm) 
S-PLY (l&a&l) 0-4£ 5-PLY(l:iW-l)0* 60* 

Figure 2-32.— Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. = angle between face grain and direction of applied stress. 

Five-ply construction, (continued) 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



89 



































r 














As 






























Y 






X 




























-j 


— 








Y 












< 




















— / 










-f 










> 




X 








































•5 


-h 










• 

















.' 




















- -1 


















































X 


- -2 
































Y\ 




< 




Ce 
















'-3 




*[ |l 


-1 


d 

























| 
















--4 










I 










































































--5 










-10 12 

scau roe % and j 





































































- J 




















































































. 






Y 







1 
















-» 1 






















0- 






V 




-f- 
















m 




' 1 


-5 




4 










-1 

Y, 







/ 






















-r' 






|L 

















































If 






































/ 




-3 




















































-•4 






































\ 














--S 






































-/ ,, 1 i 

imc rm %/m 7 i 























5-PLY{l 11 Zl)/3-- 15' 



S-PLY(l*:?-i:l)/3-90' 



Figure 2-32. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. (3 = angle between face grain and direction of applied stress. 

Five-ply construction, (continued) 




(a) 

9-PLY (ill III I I l)6- 0' 







































ii 












































3 

s 




Y 

n 

4 


It 


7 ' 








































Y 

II 


H 








'1 

11 


















— / 


















j ' 
(1 


M 


i 














































1 

















I, 


Z 
)- 
















Y\ 






--/ 










-ih 












mm 

nltim 


















\> 








."if 


X 


—z 




y 

1 


III 




4 






% 




































—3 




9 J 

1 


ill 


> 










































— 4 


























































































—5 










-10 12 
scalc route, />nr> r 























(b) 

9-PLY(l 1 1 1 1 1 1 1 15' 



Figure 2-33. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. ^ = angle between face grain and direction of applied stress. 

Nine-ply construction. 



90 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 





'a (f) 

9-PLY(llillll.li)fi- to- <3-PLY (l I I l l-I l l 75' 

Figuee 2-33. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported, (i = angle between face grain and direction of applied stress. 

Nine-ply construction, (continued) 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



91 































































\ 














— 4 














I 




















iiiii 








I 














X * 






=ji 

^dl X- 














Y 












iR3l 
HIM 




\ 


- 










mil 


— Z 


\ 
























— / 




X 




















inn 






\ 










































J 




! 











1 


\m< 


J 
















tm 






















































- 01 


Mill 






y 
























--Z 






MM 






















in 


Mil _ 

1 


— Si - ~~ 










y 






- -3 




















- -4 




































-/ 0,1 2. 
SCALE FOB % AND r 























if) 

9-PlY thbl:l:l:l:IH;l)a*tO' 




-I .1 2 
JCAl£ FOB % A/IP *■ 



(i) 

l-PlY(l:ll:l 1:1:1.1 l)a-4S' 




(h) 

9-PLY (l Z Z I 2 Z Z Z l)j3- »' 







\ 


































































— 4 
































Itttt 
















l"M 

mi 




— J 
I 






— L 












" Y 




) 

— 6 1 




< 










1 1 
















































































1 





























t 








r 


L 














MM 








hh 

MM 




















o ( 














Hill 












































- -3 




























































i(Alf FOB % 6HD 























(J) 

S Pit (i Z 1:2 Z Z Z Z l)a- 9°' 



Figure 2-33. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. @ = angle between face grain and direction of applied stress. 

Nine-ply construction, (continued) 



92 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




Figure 2-34. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported. @ = angle between face grain and direction of applied stress. 

Infinite-ply construction. 




Figure 2-34. — Curves of critical buckling constants for infinitely long rectangular plywood panels under 
combined loading. Edges simply supported, p = angle between face grain and direction of applied stress. 

Infinite-ply construction, (continued) 



94 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



6 

9 8 7 6 5 4- 3 2 

io\ 1 — —i r= — I i i i i i i — i 1 1 r 




O 0.1 01 0.3 OA 0.5 O.b 0.7 0.6 <?.9 1.0 I.I 1.2 1.3 I A 1.5 

A 
b' 



Figure 2-35. — Corrections for panel size when (3 =0°, 45°, or 90° when the panel is subjected to shear stress. 



967b545Z 



10 



06 



0.4 





























/ 

/ 

/ 

+ 


s 




^^^^^ 


N 






c 


y 














§r 

' / y 
f / // 












/' 

//. 
















— v/y j 
firsts 















OZ 04 0.6 OS 10 IZ 1.4 IA 

b 

T' 



Figure 2-36. — Corrections for panel size when panel is subjected to compression. (3=0° or 90° is a 

computed curve. (Ref. 2-12.) 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



95 































































- rf 




















V 

























































































































































































































































































ass o.b as oi 075 a a oss o.9 tm i.o 

Figure 2-37. — Buckling of infinitely long plates 
of symmetrical construction under uniform shear. 
Edges simply supported. The constant A' s oo plot- 

E fw 

ted as a function of the ratio -. 



Ef W -\-Ef X 



z.o 

1.6 

1:6 
1.4 
1. 1 

% 

^J.O 

0.8 
O.i 

0.4 
0.2 










































































A. 























































































































































JU 0.55 0.6 065 0.1 015 0.8 0.65 0.9 0.95 1.0 
Lb* 



Figure 2-39.— Buckling of infinitely long plates 
of symmetrical construction under uniform com- 
pression. Edges simply supported. The constant 



E 



Kctx plotted as a function of the ratio - 



fx 

































































■-FACt 


,.n> 


V IN, 




HI ■ 


SI0H 












































< 























































































































OS OSS Qi 0&f> 07 075 08 OSS 0$ 09$ iQ 



Figure 2-38. — Buckling of infinitely long plates 
of symmetrical construction under uniform shear. 
Edges simply supported. The constant b'/a plot- 

Ef W 

ted as a function of the ratio . 

E/ w -\-Ef X 



2-V 
1.8 

16 

1.4 

II 

6 
Oi 
4 
2 



Efw+E JX 



OS 055 Ob 065 0.7 75 06 06S 09 095 W 

Figure 2-40. — Buckling of infinitely long plates 
of symmetrical construction under uniform com- 
pression. Edges simply supported. The constant 

Ef W 

b'/a plotted as a function of the ratio . 

E fw +E fx 



96 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



2.72. Allowable Shear in Plywood Webs. 

2.720. General. Beams are required to have a high strength-weight ratio and, there- 
fore, they are generally designed so that they will fail in shear at about the load which 
will cause bending failures. A higher strength-weight ratio is usually obtained if the 
beams fail in bending before shear failure can occur. 

Plywood when used as webs of beams is subjected to different stress conditions from 
those when it is used in simple shear frames. It is essential, therefore, that tests to deter- 
mine the strengths of shear webs be made upon specimen beams designed with flanges 
only sufficiently strong to hold the load at which shear failure is expected. Plywood 
webs tested in heavy shear frames with hinged corners will give shear strengths that are 
too high for direct application to beam design. 

In any case where buckling is obtained, the stiffeners must have adequate strength 
to resist the additional loads due to such buckling, and the webs must be fastened to 
the flanges in. such a manner as to overcome the tendency of the buckles in the web to 
project themselves into this fastening and cause premature failure. 

*2.721. Allowable shear stresses. The allowable shear stresses of plywood webs 
having the face grain direction at 0°, 45°, or 90° to the main beam axis may be obtained 
from figure 2-41. 

The direct use of figure 2-41 for any type of beam having 45° shear webs has been 
verified by numerous tests of I- and box-beams. A few exploratory tests of beams having 
0° and 90° plywood shear webs has indicated that the allowable ultimate shear stresses 
obtained for these constructions by using figure 2-41 are conservative. Until sufficient 
additional tests have been conducted to establish a more rational method of determining 
the allowable ultimate shear stress for plywood shear webs in which the face grain makes 
an angle of 0° or 90° to the longitudinal axis of the beam, values obtained from figure 
2-41 should be used. 

Plywood shear webs of 45° are more efficient than 0° or 90° webs. 

The designer is cautioned that box beams may fail at a load lower than that indi- 
cated by the strength of the webs as shown in figure 2-41, because of inadequate glue 
areas of webs at stiffeners or flanges. Such premature failures result from a separation 
of the web from the flanges or stiffeners. Additional information for guidance in stiffener 
design is presented in reference 2-7. 

Figure 2-41 contains a parameter a/b in the form of a family of curves. The a/b = l 
curve represents a spacing between stiffeners just equal to the clear depth between flanges. 
The curves below a/b = 1 should be used for the design of shear webs of beams whose 
stiffener spacing exceeds the clear distance between flanges. The upper set of curves 
should be used for the design of beams whose stiffener spacing is less than the clear dis- 
tance between flanges. 

Although, in a strict interpretation, the curves in figure 2-41 apply only to plywood 
webs of beams, it is believed that they may also be used to calculate the shear strength 
of other types of plywood shear panels (such as in wing skins, or fuselage coverings 
having little or no curvature) provided certain precautions are taken. If any edge of a 
panel is not rigidly restrained against movement in its own plane, the lowest curve 
(a/b = 0.2) should be used. An example of this may be a plywood panel in the wing 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



07 



covering at the inboard end of an outer panel where 1 the end rib does not afford a rigid 
span wise support to the edge of the panel. The shear strength of a panel that is rigidly 
restrained along all edges in its own plane may be determined by use of the o/h = 1.0 
curve. A panel whose edges are entirely within a larger plywood sheet, or a panel that 
is restrained on one or more sides by a heavy member, such as a beam-flange, and on 
all other sides by a continuation of the plywood, will fall in this group. 

Further tests and studies will be made to ascertain if these applications of the curves 
in figure 2-41 can be made in addition to its use for the design of plywood shear webs 
of beams. 

2.722. Use of figures 2-41 and 2-42. The abscissa of figure 2-41 is the ratio a/a 
where « = either clear distance between flanges or clear distance between stiff eners 
(sec. 2.701). 

fl = the width of a hypothetical panel of length h which will buckle at a shearing 
stress of F»$. 



The procedure to be followed in the use of figures 2-41 and 2-42 is as follows: 

(1) Knowing the panel dimensions a, b, and t and the plywood species, read the 
values of F s o, K so o , and b'/a from tables 2-9 and 2-10. For plywood species and construc- 
tions not listed in tables 2-9 and 2-10 F sg may be calculated from equations in section 
2.612 and A~ s0 o and b'/a may be read from figures 2-37 and 2-38 once E fw and E fx are 
determined by test or from equations in section 2.52. K sX and b'/a may also be read 
from the intercepts of figures 2-29 and 2-34 if desired. (Sec. 2.702.) 

(2) Calculate a/6 and a/t. 

(3) Calculate b/b' and read K sO0 /K s from figure 2-3.5. Calculate K s . 

(4) From figure 2-42, read a/a as follows: (or a may be calculated from equation 
2:69 if preferred). 

(a) Draw line (1) connecting the appropriate El (for species of face plies), 
and F s q. 

(b) Pivot at scale (1) (2) and draw line (2) to the value of K s determined in 
the third step. 

(c) Pivot at scale (2) (3) and draw line (3) to the value of a/t found in the 
second step. 

(d) Read the value of a/a from the intercept on the a/a scale. 

(5) The allowable shear stress (F„) for the web can then be obtained hi terms of 
Ff/F a o from figure 2^41. (For a/a values greater than 4.0, the a/b curves may be ex- 
trapolated as straight lines to meet at a point corresponding to a/a a = 10 and F s /F s e =0.2. 



98 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



99 




100 



ANC BULLETIN — DESIGN OP WOOD AIRCRAFT STRUCTURES 



*2.72 3. Buckling of plywood shear webs. In connection with shear web tests on 
various types of beams, it was observed that for plywood webs in the a/a range of 
less than 1.2, buckling was of the inelastic type which often caused visible damage soon 
after buckling and sometimes just as the buckles appeared for those webs designed to 
fail in the neighborhood of F s e- No accurate criteria can be presented at this time but 
the designer is cautioned to avoid the use of webs that may be damaged by buckling 
before the limit or yield stress is reached. The buckling curve established by these 
tests is shown in figure 2-41. Additional information on buckling of plywood shear 
webs is given in Forest Products Laboratory Mimeograph 1318-B (Ref. 2-8.) 

2.73. Lightening Holes. When the computed shear stress for a full depth web of 
practical design is relatively low, as in some rib designs, the efficiency, or strength- 
weight ratio, may be increased by the careful use of lightening holes and reinforcements. 
General theoretical or empirical methods for determining the strength of plywood 
webs with lightening holes are not available, and tests should, therefore, be made for 
specific cases. The effects of lightening holes in typical rib designs are discussed in 
N.A.C.A. Technical Report 345 (ref. 2-23). 

*2.74. Torsional Strength and Rigidity of Box Spars. The maximum shear 
stresses in plywood webs for most types of box spars subjected to torsion may be 
calculated from the following formula: 



(2:70) 



b' t(C'-2b') 



where: 

t = thickness of one web. 

b'=mean width of spar (total width minus thickness of one web). 
C = average of the outside and inside periphery of the cross section. 
The allowable ultimate stress in torsion of plywood webs is determined as in 
section 2.721. 

The torsional rigidity of box beams up to the proportional limit, or to the buckling 
stress (whichever is the lesser) is given by the formula: 



(i -±Gtb' T (C'-2b')* i2:71) 



2.7 5. Plywood Panels under Normal Loads. 

2.7 50. General. When rectangular plywood panels, which have the face grain 
direction parallel or perpendicular to the edges, are subjected to normal loads, the 
deflections and in some cases the stresses developed, are given by the following 
approximate formulas. If the maximum panel deflection exceeds about one-half its 
thickness, the formulas for large deflections will give results which are somewhat more 
accurate than those given by the formulas for small deflections. 



STRENGTH OP WOOD AND PLYWOOD ELEMENT 



1(11 



2.751. Small deflections. 

(a) Uniform load — all edges s 



imply supporte* 




(2:72) 



where: 

\o = deflection at center of panel. 

p = load per unit area. 

a = width of plate, (short side) 
K, = constant from figure 2-43 (a). 

The maximum bending moment at the center of the panel on a section perpendicular 
to side a may be obtained from figure 2-43 (b). The maximum bending moment on a 
section perpendicular to side b is given by the same curve, provided a and b, and Ex and 
Eg are interchanged in the abscissa, and a is replaced by b in the ordinate. The 
corresponding stresses can be calculated from the formulas given in section 2.614. 

(b) Uniform load — all edges clamped. 



to = 0.031 A'„ 



2 Eft 



(2:73) 



where: 



Ki= constant from figure 2-43 (a). 

(c) Concentrated load at center — all edges simply supported. 




(2:74) 



where : 



A's = constant from figure 2-43 (a). 



2.752. Large deflections. 

(a) Uniform load — all edges simply supported. 

The relation between the load and deflection is given by the formula: 



p = K i E L w -j+A' 5 E L w a s — 



(2:75) 



where : 



Ki and K 5 are constants whose approximate values are given in table 2-11. 
E L is taken for the species of the face ply. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



103 



The maximum bending moment at the center of the panel can be calculated from 
the following approximate formula provided the length of the panel exceeds its width 
by a moderate amount: 

M max . = Xi Ei Wo -p~2 (long narrow panels only) (2:76) 



where: 

X x = constant from figure 2-43 (c). 

Although the edge support conditions are taken as simply supported, it is assumed 
that the panel length and width remain unchanged after the panel has been deflected. 
Therefore, in addition to the bending stress, there will be a direct tensile or membrane 
stress set up in the plane of the plywood, and the total stress in any ply will be the 
algebraic sum of the bending stress and direct stress in that ply. The maximum total 
stress will occur in the extreme fiber of the outermost ply having its grain direction 
perpendicular to the plane of the section upon which the moment was taken; the bend- 
ing stress being calculated from section 2.62, and the direct stress from section 2.601 
after first determining the average direct stress across the section from the formula: 

ftUi ) = 2.55 E n (—) (long narrow panels only) (2:77) 



(b) Uniform load — all edges clamped. 

The load-deflection relation, formula 2:75, will also apply to this case provided 
Kg and Ki from table 2-11 are substituted for and K$, respectively. The maximum 
total stress may also be determined as outlined in (a) above, provided X2 from figure 
2-43 (c) is substituted for Xi in formula 2:76. 

2.76. Stiffened Flat Plywood Panels. 

*2.760. Effective Widths in Compression. Because of the edge restraint afforded by 
the stiffeners in stiffened panels, the ultimate stress or the fiber stress at the proportional 
limit may be greater than the critical buckling stress of the sheet between stiffeners. 
For convenience it is assumed that the sheet, which is under a variable stress, can be 
replaced by effective widths acting in conjunction with the stiffeners at the same deforma- 
tion (but not necessarily the same stress). The remaining area of the sheet is considered 
as being ineffective. The total effective width of sheet for any stiffener is made up of 
increments w (measured from the outside edges of the stiffeners) plus the width of the 
stiffener (see sketch on fig. 2-44). 



104 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



Table 2—11. — Values of constants in the approximate deflection formulas for plywood panels under normal 

loads 1 



Panel construction 2 


Uniform load all edges 
simply supported 


Uniform load all edges 
clamped 




(6 la) 


Ki 


Ke 


(b/a) 


K'i 


A'r 


3-ply, = 0° 


1 

1.5 
2.0 
>3.0 

>1 


(see ( 
1.7 

.9 
. 5 


= 90°) 

5.9 
4.7 
4.7 


1.0 
2.0 
>3.0 


(see i 

3.6 
2.5 


» =90°) 

6.0 
7.0 


= 90° 


0.3 


13.3 


1.0 
>2.0 

1.0 
2 

>3 
1.0 

>2 


33.3 
32.0 


27.9 
19.2 


5-ply, 0=0° 

=90° 


1.0 
1.5 

>2.0 
1.0 

>1.5 


(see t 

2.4 
1.5 
6.2 

5.0 


= 90°) 

6.5 
6.0 
12.3 
10.0 


(see ( 

8.3 
7.9 
28.7 

26.5 


1 =90°) 

8.2 
9.4 
17.7 
15.5 



1 The values given in this table are for spruce plywood, all plies of equal thickness, but they may also be considered 
applicable to plywood of other species and of the same constructions. For plywood made of more than five plies or of 
unequal ply thickness, the above table may be used as a rough guide in arbitrarily selecting values of these constants. 

- is the angle between the face grain direction and side b of the panel. 




LEGEND' 

A- AVERAGE STRESS IN PLATE AT PROPORTIONAL LIMIT -r PROPORTlONAL-LIMlT STRESS Of MATERIAL 
^ AT PROPORTIONAL-LIMIT STRESS. PACE GRAIN AT O'OR 90' TO LOAD 

3- AVERAGE STRESS IN PLATE AT MAXIMUM LOAD ~ MAM MUM STRESS Or MATERIAL = 
^J* AT ULTIMATE STRESS PACE GRAIN AT 0' OR 90' TO LOAD . 



C- AVERAGE STRESS IN PLATE AT MAXIMUM LOAD - MAXIMUM STRESS OP MATERIAL ' 
" ' AT ULTIMATE STRESS PACE GRAIN AT 45° TO LOAD 




I Z 3 4- 5 b 7 8 9 

PROPORTIONAL- LI MIT 5TRE55 OF MATERIAL t COMPUTED BUCKLING STRESS 



Figure 2-44. — Effective-width curves for flat plywood panels in compression. 



Ill the use of figure 2-44, the fiber stress at proportional limit, F cp , is equal to F CPW 
when the face grain is parallel to the stiff eners, or F cpx when the face grain is perpen- 
dicular to the stiffeners. These values may be obtained from table 2-9 or section 2.600. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



105 



When the face grain is 45° to the stiffeners, F ep a may be taken as 0.55 F cu4i , where 
F cut $ is determined by section 2.610. The critical buckling stress F, w is determined bi- 
section 2.701. The procedure for determining effective widths depends upon the range 
of stresses under consideration, as follows: 

(1) For plywood stresses up to the critical buckling stress, the effective width ratio 
(2w/a) may be taken as equal to 1 except when the critical buckling stress is near the 
proportional limit of the plywood. This proportional limit may be reached locally when 
the average stress is somewhat below the proportional-limit value because of nonuniform 
stress distribution across the panel. 

(2) Whenever the stress at the edge of the panel (in the plywood adjacent to the 
stiffener) exceeds the proportional limit for the plywood, the effective width is determined 
from the curves of figure 2-44, or by interpolating between them, depending upon the 
magnitude of the edge stress. 

(3) Whenever the stress at the edge of the panel is between the critical buckling 
stress of the panel and the stress at proportional limit for the plywood, the effective width 
is given by the formula: 

2w/a Jl~K)F F +mF dp -F c , r ) f2;781 

J\r, p " c lT ) 

where : 

/v= value of 2w/a from curve in figure 2-44 at the ratio F rp /F 0cr . 
f = any stress between F, w and F cp . 

This formula does not apply when the critical buckling stress is near or above the 
stress at proportional limit. 

*2.76l Compressive strength. The strength of stiffened flat plywood panels may 
be determined by the following method when the stiffeners and their effective widths of 
sheet are assumed to act as columns. The effective width of sheet must first be deter- 
mined as mentioned in section 2.760 after which the following procedure may be used. 
The effective modulus of elasticity (£") of the composite section (stiffener plus effective 
sheet) is given by the formula: 

E , = E b A p +E Le A, t 

A. 

where : 

E b = E w for face grain parallel to stiffeners. 

= E X for face grain perpendicular to stiffeners. 
For 45° face grain, see section 2.5611. 
El c pertains to the species of the stiffener. 
i4 P = area of effective panel. 
^4 S ( = area of stiffener. 
A=A P + A sl . 

The effective moment of inertia (/') of the composite section is given by the formula : 

r= Y' Ip+ W A " ( x-t H) 2+ ir Mi (x ~ v)2 (2:80) 



106 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



where : 

Ei = E fw for face grain parallel to stiff eners. 

= E fx for face grain perpendicular to stiffeners. 
For 45° face grain use equation 2:63, section 2.6140. 
I r = I of effective panel about its own neutral axis. 

= (2w+b)tyi2. 
I s t = I of stiffener about its neutral axis. 
/= thickness of panel. 
d = depth of stiffener. 

y = distance from the neutral axis of the stiffener to the stiffener face away from 
the panel. 

x = distance from the neutral axis of the composite section to the stiffener face away 
from the panel. 

E b A p {d+-)+E Lc A st y } 

= E b A p +E^,~A~~t 

The internal or calculated averag^stress over the composite section will be P/A, 
which should not exceed the allowable stress determined from the following formulas: 

Long Columns: 

10E' 

Fc= (L'uy psi ( 2:82) 

where : 

L'=L/V~ 
9 = V~T7~A 



(L'/ 9 ) cr = V 15E'/F CU 

F 

F CU = E' -—- when the stiffener is critical. 

E Lc 

F 

= E' -~- when the plywood is critical. 

■£<& 



F cu b = F cuw when face grain is parallel to stiffeners. 

=F CU x when face grain is perpendicular to stiffeners. 
= F cu q when face grain is at an angle to stiffeners. 

When the direction of column bowing is unknown, use the minimum value of F cu 
determined for the plywood or the stiffener itself. When the direction of column bowing 
is known, the value of F cu for the material on the inside of the curvature may be used. 

The value chosen for the fixity coefficient, c, depends on the behavior of the structure 
of which the panel is a part, or on the test set-up, as the case may be. See section 3.1382 
for typical values in structures. In carefully made flat-ended test panels, a fixity of 
c = 3.0 or more is usually developed. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



107 



Short columns: 

ft-R.[i-|(0]p»- (MB) 

where: 

K = (L'/ 9 ) cr 

F cu is same as for long columns when L'/ p approaches (L'/ p) (r . When L'/p is fairly- 
small, F r „ should be taken as the minimum in the composite section in the longitudinal 
direction. This minimum may occur in the plywood or in the stiffener itself. 

*2.76l0. Modes of failure in stiffened panels. The procedure in section 2.761 for 
short columns assumes that a stiffened panel fails at the instant any longitudinal fiber 
of the composite section reaches its crushing stress, based on relative moduli of elas- 
ticity. Such composite constructions may actually develop an ultimate strength corre- 
sponding to this assumption, or higher or lower strengths, depending on several factors, 
some of which are discussed in the following. 

A possible mode of failure, which has been investigated for only one particular type 

of construction, is the premature separation of the plywood panel from its stiffeners 

occurring when the forces required to restrain the edges of the buckled panels become 

too great for the strength of the plywood or its attachment to the stiffeners. (Ref . 2-10. ) 

A comparison of the results of this limited investigation with the method of section 2.761, 

however, shows the latter to be only slightly unconservative in the worst case. This 

comparison also indicates that section 2.761 may be conservative when separation is 

F F 
prevented and the ratio — — for the stiffeners is higher than — ^- for the plywood. 

El c Eb 

Since no criteria suitable for general application are available for predicting the 
critical modes of failure, it is recommended that typical panels of each particular type 
of construction be tested. 

A more general investigation of this problem is now under way at the Forest Products 
Laboratory. 

*2.762. Bending. The maximum bending stress in stiffened plywood panels can be 
calculated from the following formula, when the face grain direction is 0° or 90° to the 
direction of the span: 

A ™£ (2:84) 

where : 

c' = distance from the neutral axis of the composite section to the extreme longitu- 
dinal fiber. 

El is taken for the species of the outermost longitudinal fiber. 

This maximum bending stress should not exceed the modulus of rupture of the ma- 
terial in which the maximum stress exists. If the stiffener is of an I or box section, 
the modulus of rupture must be corrected by a form factor as follows: When the load 
is applied so that the outer flange of the stiffener will fail in compression, the proper 
form factor to use is that for a beam having the same flange dimensions as the outer flange 
of the stiffener, and the same web thickness as the stiffener, but of a depth equal to 2x. 
If the load is applied so that the panel will fail in compression, the proper form factor 



108 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




STRENGTH OF WOOD AND PLYWOOD ELEMENTS 109 

to use is that of a beam having flange dimensions equal to that of the effective sheet 
plus the flange of the stiffener adjacent to the panel, and a web thickness equal to that 
of the stiffener but a depth of 2{d+t— x). In either case no form factor need be used 
if the neutral axis lies within the compression flange. 

Formula 2:84 will apply to stiffened panels having the face grain direction 45° to 
the length of the stiffener if E', El, and /' are adjusted as indicated for the 45° com- 
pression case. 

2.8 CURVED PLYWOOD PANELS. 

**2.80. Buckling in Compression. No information other than the test results on 
a few types of plywood construction having the face grain parallel to the length can be 
given on the buckling of curved plywood panels in compression. The curves given in 
figure 2-45 represent the averages of the test results obtained on curved panels by the 
Hughes Aircraft Company on the plywood constructions noted. The actual const ruc- 
tions tested were essentially three-ply, with the veneers being laminated in the face, 
back, and core when the total number of veneers was greater than three. Large positive 
deviations from the curves were obtained when the panels did not buckle before the ulti- 
mate load was reached. For purposes of design, it is recommended that the values from 
the curves of figure 2-45 be divided by 1.15. 

Other tests indicate that when the width of a curved panel is greater than 30° of 
arc, the buckling stress is approximately the same as that of a complete cylinder of the 
same construction and radius of curvature, and may be computed as indicated in sec- 
tion 2.820. 

*2.81. Strength in Compression or Shear; or Combined Compression (or Ten- 
sion) and Shear. When failure by buckling does not occur, the ultimate strength of 
curved plywood panels subjected to compression or shear, or combined compression (or 
tension) and shear may be obtained by the method given in section 2.613. This method 
is applicable when the face grain direction is at any angle. - 

2.82. Circular thin-walled plywood cylinders. (Ref. 2 — 14). 

2.820. Compression with face grain parallel or perpendicular to the axis of the 
cylinder. The theoretical buckling stress for a long cylinder (to be modified for design 
as described later in the section) is given by the formula: 

F*r (theoretical) = k E L - (2:85) 

where : 

El is for the species of the face plies. 
t = thickness of plywood 
r = radius of cylinder 

k is a buckling constant that is a function of „ and is determined from figure 

ifj\-\-rLi 

2-46. In using figure 2-46, Ei is the flexural stiffness of the plywood in the direction 
parallel to the longitudinal axis of the cylinder. E\ is equal to E fu> when the face grain 
is longitudinal and is equal to E fx when the face grain is circumferential. Ei is the flex- 
ural stiffness of the plywood in the circumferential direction. E^ + Eo is equal to E rw +E fI . 



110 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



Figure 2-46. — Theoretical curve for long, thin plywood cylinders in axial compression. The ordinates 

represent k in the formula P=k E - where P is the buckling stress. The abscissas represent the ratio 

r 



E l 



- where E\ and Eo are the flexural stiffnesses of the plywood. 



Because of the steepness of the curve for k at the extreme right and left portions, it 
appears advisable to avoid, when possible, the use of types of plywood for which the ratio 
Ei 

is small or nearly equal to unity. 

E \-\-E% 

For use in design, the theoretical buckling stress must be modified as the propor- 
tional-limit stress is approached. This is accomplished by the use of figure 2-47. The 
proportional-limit stress used with this chart is the compressive proportional limit for 
the plywood in the direction of the cylinder axis and is determined from table 2-9 or 
from section 2.600. F CP = F CPW when the face grain is longitudinal. F cp = F cpx when the 
face grain is circumferential. The chart is entered along the abscissa with the ratio 
F, ,, r (theoretical) /F cp . The design buckling stress, (F Ccr ), is then obtained by multiplying 
the ordinate by F cp . 

Tests indicate that an increase in strength may be expected when the ratio of length 
to radius is approximately one or less. This effect is being further investigated. 
Limited amounts of double curvature have negligible effect on buckling stress. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



111 




0.1 02 0.3 0.* OS 06 01 08 09 10 /./ II /.3 M IS IA U 

T HEORETICAL BUCKLING STRE.5S ( F c CJ . THEORETICAL) 
PROPORTIONAL LIMIT 5TP£5S \ ' 

Figure 2-47. — Design curve for long, thin-walled plywood cylinders. 

*2.821. Compression with 45° face grain. When the face grain is at an angle of 
45° to the cylinder axis, the theoretical buckling stress may be taken as the average of 
the theoretical buckling stresses obtained by assuming the face grain direction to be: 
(1) Parallel to the cylinder axis, (2) circumferential. In using figure 2-47, however, to 
obtain the design buckling stress, the proportional-limit value (F cp ) should be that for 
the plywood at 45° to the face grain. F rpii may be taken as 0.55 F cui; „ where F cui5 is 
determined by section 2.610. 

2.822. Bending. For bending, the design buckling stress determined as for com- 
pression may be increased 10 percent. 

*2.82 3. Torsion. No data on buckling in torsion, suitable for general application, 
are yet available. The shear strength when buckling does not occur may be determined 
by section 2.612. 

2.824. Combined torsion and bending. When design buckling stresses for pure 
torsion and pure bending are available, cases of combined loading can be checked by 
the following interaction formula: 

(£) + 

Where : 

f,t = applied torsional shear stress. 
fb= applied bending stress. 
F slc1 =pure torsion design buckling stress 
F 6cr = pure bending design buckling stress 



112 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



WIDTH OF WOOD MLMBER IN INCHES 
1 2 3 4 5 6 7 




4i>8/0 
WIDTH OF WOOD MEMBERS IN INCHES 



Figure 2-48. — Bearing strength of bolts in spruce parallel to grain. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



113 



WIDTH OF WOOD MEMBER IN INCHES 
12 3 4 5 6 7 




BOL TS IN SPRUCE . SEE SEC TION 2. 902 FOR 
BEARING STRENGTH OR OTHER SPECIES. FOR 
!Hj[ |'i) ECCENTRIC LOADING (APPLIED ONLY AT ONE END 
jjj] OF BOL T) DIVIDE LOAD FROM CURVES BY 2. 

BROKEN CURVES APPLY WHEN ALUMINUM- 
:| ALLOY BUSHINGS ARE USED (5LE SECTION 230$. 

i;:;lti!itniHm;t!iHi?i;;p;;;f;;;:i::::n;;;i;;;tfff '•• 




20 



IB 



14 



10 



y 

I 



4 6 6 10 

WIDTH OF WOOD MEMBER IN INCHES 



12 



14 



Figure 2-49. — Bearing strength of bolts in spruce perpendicular to grain 



114 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



2.9. JOINTS. 
2.90. Bolted Joints. 

2.900. Bearing parallel and perpendicular to grain. In determining the sizes of 
solid steel aircraft bolts to be used in wood, the strength of the wood in bearing against 
the bolts can be obtained from the solid curves of figures 2-48 and 2-49. Broken curves 
are for use in determining bearing loads of aluminum bushings used in combination with 
steel bolts. (Sec. 2.906.) These curves give the allowable ultimate loads for standard 
aircraft bolts bearing in spruce, and applied concentric with the centerline of the member, 
that is, with the load divided equally between the two ends of the bolt. The allowable 
ultimate eccentric loads, that is, those applied at one end of the bolt only, are one-half 
the loads given by these curves. 

The value of bolt bearing stress at proportional limit when bearing perpendicular 
to the grain is affected to only a slight extent by the L/D ratio. In general, this value 
may be found with sufficient accuracy by dividing the ultimate bearing strength by 1.33 
for all L/D ratios (sec. 2.1000). 

When the bearing is parallel to the grain, however, the value of bolt bearing stress 
at the proportional limit varies considerably with the L/D ratio. The bearing stress at 
proportional limit then drops rapidly with an increase in L/D, becoming, at an L/D of 9, 
less than 50 percent of the bearing stress at proportional limit at an L/D of 1. The crush- 
ing stress of softwoods parallel to the grain is equal to 1.25 (1.33 for hardwoods) times 
the bearing stress at proportional limit, for L/D ratios from to 1, and increases linearly 
to 1.7 times at an L/D of 12. This relation, or the factors by which the ultimate bearing 
loads parallel to the grain must be divided to obtain the bolt load at proportional limit, 
is given in figure 2-50. 



17 \i Mi¥¥¥Win 
$ ^ - - — .--7 • 

•" t — - 

^ £ :::: 

VS <»: :t:: :::: J .. . 

1 1 ; J^- 

t K ....iinii 


[Et- :: : ::: -v^p- ; : : 

<*" iiii ii'ii 


m * : . 

:: 

1 ..Tintlga 


'T ; 

- ^ 

iilll 



#^ 

1 ' 


■"" 


iif iiii^n 

^ ■■ „ 

5 £ /./ - :...| .'....■:):. — 

1.0 1 — 1 

0/23 


- — -'■ -- h }■■■ 

m. If m m Htr mm m m m 

r. • :■ r% ; : if?;ii ,, ' , 

tt:: ': -t:: : . : : : ! . ; !;! pi j 
< S 6 7 a 


ttft:: 

H — - ' 

(tttt . . 

:: :: 

■■ M : 
9 10 


r .... - 

•! Mil j 

. .. -f; 
II 


rr|||f If 
■ 

T ffiT +i+t -KH 
/2 /J 


;j 

:B| 

:±U 
:::: 

OF 



BEARING LENGTH + BOLT DIAMETER f L /p RATIO) 



Figure 2-50. — Variation of the ratio of ultimate bearing strength to bearing strength at proportional 
limit with L/D for bolts bearing parallel to grain. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



115 



9 liiiijiiiilHi ;[:;:. I::;; ;::|:;-; 

r ;■ :::: ;:!; -U-u^ tin. 




'4 '2 '4 ' c 4 

DIAMETER OF CIRCULAR PLATE IN INCHES 



Figure 2-51. — Bearing strength of steel washers in spruce — perpendicular to grain. 



Some designers may prefer to work in terms of bearing stress rather than bearing- 
load. Figures 2-52 and 2-53 show the ratio of ultimate bearing stress to ultimate com- 
pressive stress for bolts loaded parallel and perpendicular to the grain of the wood. The 
curves showing ultimate bearing stress parallel to the grain show two cut-offs, one for a 
ratio of ultimate stress to proportional limit stress of 1.5 and the other for a ratio of 1.7. 
The bolt load curves of figures 2-48 and 2-49 are based on the 1.7 cut-off. It is recom- 
mended that the 1.5 cut-off curve be used if no fitting factor is used in the analysis of 
the bolted connection. If a fitting factor is used, the 1.7 cut-off factor can be used with 
safety. 

2.901. Bearing at an angle to the grain. When the load on a bolt is applied at an 
angle between 0° and 90° to the grain, the allowable load (proportional limit or ultimate) 
may be computed from the expression 

N= — (2:87) 

1 P sin* 6+Q cos 2 6 K } 

where : 

N = The allowable bolt load at angle 6. 
P = The allowable bolt load parallel to the grain. 
Q = the allowable bolt load perpendicular to the grain. 
6 = the angle between the applied load and the direction of the grain. 
Equation 2:87 is solved graphically by the Scholten Nomograph, figure 2-54. 



116 



ANC BULLETIN— DESIGN OF W OOD AIRCRAFT STRUCTURES 



10 
9 
06 

0.7 
Ob 
0.5 
04 

03 
0.2 

0.1 

















































VARIATION IN RATIO OF ULTIMATE 
BEARING 5TRE55 TO ULTIMATE COM- 
PRESSIVE STRESS PARALLEL TO GRAIN 
WITH VARIATION IN ^ RAT 10 


































































\ 


































\ 






cu~, 


r -OFI 


/ 




7 












CO 


T- OF 


~F AT 


F brp 

















































































































































10 



12. 



BEARING LENGTH -r DIAMETER ( RATIo) 

Figure 2-52. — Bolt bearing stresses parallel to grain. 



lb 



II 

ft 

kj 



20 
IS 
16 

1.7 
1.6 
1-5 
1.4 
1.3 
IZ 

U 

10 



fa RATIO 
10 II IZ 13 14 IS lb 



















































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DIAMETER OF WASH LR OR BOLT~D (INCHES) 
Figure 2-53. — Bolt bearing stresses perpendicular to grain. 



STRENGTH OF WOOD AND 



PLYWOOD ELEMENTS 



117 




118 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



2.902. Bearing in woods other than spruce. The allowable ultimate loads for 
bearing of bolts in some species of wood other than spruce may be determined by 
multiplying the loads from figures 2-48 and 2-49 by the factors given in table 2-12. 
When the bearing stress curves of figures 2-52 and 2-53 are used, these correction factors 
need not be applied. (The value of K discussed in section 2.904 is also given in this 
table.) These factors have been obtained by the following method which can be used 
to obtain factors for species not listed in this table. The factor for loads parallel to the 
grain is the ratio of the allowable compressive stress at the proportional limit for the 
species to the corresponding allowable for spruce. The proportional limit stresses for 
compression parallel to the grain are given in column 11, table 2-3. For compression 
perpendicular to the grain the proper factors can be obtained by using the ratio of the 
crushing strengths in column 13, table 2-3, as these values are proportional to the 
proportional limit values. 



Table 2-V2. — Bearing .strengths of other species as compared to spruce 





Parallel 


Perpendicular 




Species 


to grain 1 


to grain 




Spruce 


1 .00 


1.00 


1.00 


Douglas-fir (coast tvpe) 


1.40 


1 .55 


1 30 


Fir, noble 


1.02 


1.02 


1.11 


Hemlock, western 


1.18 


1 .13 


1 .09 


Pine, eastern white '. 


.96 


93 


1 .12 


White-cedar, Port Orforrl 


1 22 


1.23 


1.20 


Birch 


1 .37 


1 89 


.79 


Mahogany 


1.22 


2 10 


1 .06 


Maple 


1 .40 


2.58 


.69 


Walnut 


1.42 


2.06 


1 .07 


Yellowpoplar ■ 


.94 


.96 


.88 



1 These values for hardwoods apply only at the proportional limit. At the ultimate bearing strength they should be 

multiplied by the ratio between the ordinates of the curves for hardwoods and softwoods at the appropriate — ratio in 
figure 2-50. D 
- See section 2.904. 



2.903. Combined concentric and eccentric loadings; bolt groups. When the de- 
sign loads on a group of bolts are either all concentric or all eccentric and are all in the 
same direction, the allowable loads for the individual bolts may be added directly to 
determine the total allowable load for the group. When the design loads are in different 
directions (as when the load causes a moment about the centroid of the bolt group) or 
when they are partly concentric and partly eccentric, each bolt must be treated separ- 
ately. The design loads and moments must be distributed to each bolt in proportion to 
its resistance and the geometry of the bolt group. This often requires a trial and error 
calculation. 

2.904. Bolt spacings. The following bolt spacing criteria are based on spruce. 
For other species, these spacings should be multiplied by the factor K in table 2-12 or 
by the expression: 

K =wk„ < 2:88) 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



119 



where : 

F cp = allowable stress at proportional limit in compression parallel to the grain. 
F su = allowable shearing stress parallel to the grain of the material. 

2.9040. Spacing of bolts loaded parallel to the grain. 

(1) Spacing parallel to the grain. The minimum distance from the center of any 
bolt to the edge of the next bolt in a spruce member subjected to either tension or com- 
pression is given in figure 2-55. The minimum distance from the edge of a bolt to the 
end of a spruce member subjected to tension is also given by this figure. 

The minimum distance from the edge of a bolt to the end of a member subjected 
to compression should be bolt diameters. 

(2) Spacing perpendicular to the grain. The minimum distance between the edges 
of adjacent bolts or between the edge of the member and the edge of the nearest bolt 
should be one bolt diameter for all species. However, pending further investigation of 
the effects of stress concentration at bolt holes, it is recommended that the stress in the 
area remaining to resist tension at the critical section through a bolt hole not exceed 
two-thirds the modulus of rupture in static bending when cross-banded reinforcing 
plates are used; otherwise one-half the modulus of rupture shall not be exceeded. 

(3) When a bolt load is less than the allowable load parallel to the grain, the spacing 
may be reduced in the following way: The bolt spacing given in figure 2-55 can t be 
multiplied by the ratio of actual load to allowable load except that the spacing should 
be not less than three bolt diameters. The bolt spacing perpendicular to the grain 
cannot be reduced below one bolt diameter. 

2.9041. Spacing of bolts loaded perpendicular to the grain. 

(1) Spacing perpendicular to the grain. The minimum distance from the edge of a 
bolt to the edge of the member toward which the bolt pressure is acting should be 3 % 
bolt diameters. The margin on the opposite edge and the distance between the edges 
of adjacent bolts should be not less than one bolt diameter. 

(2) Spacing parallel to the grain. The minimum distance between edges of adjacent 
bolts should be three bolt diameters and the distance between the end of the member 
and the edge of the nearest bolt should be not less than four bolt diameters. 

(3) When a bolt load is less than the allowable load perpendicular to the grain, all bolt 
spacings may be multiplied by the ratio of actual load to allowable load except that the 
spacing should be not less than one bolt diameter. The distance between the end of the 
member and the edge of the nearest bolt, measured parallel to the grain, should be not 
less than three bolt diameters, however. 

2.9042. Spacing of bolts loaded at an angle to the grain. When bolts are loaded 
at some angle to the grain, the load can be resolved into components parallel and 
perpendicular to the grain and the spacings thereafter determined in accordance with 
paragraphs 2.9040 and 2.9041. 

2.9043. General notes on bolt spacing. When bushings are used in combina- 
tion with bolts, the spacing should be based upon the outside diameter of the bushing. 
When adjacent bolts or bushings are of different diameters, the spacing should be based 
upon the larger. 

When staggered rows of bolts are employed in design, the minimum distance between 
the center lines of adjacent bolt rows should be not less than the sum of the diameters 
of the largest bolt in each row. 



120 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




O / 2 J 4 s 6 7 8 9 /O // /2 /3 14 



t -FWC/</V£5S OF WOOD M£MS£f? /MCHES 

Figure 2-55. — Allowable distances between bolts and allowable end margin for bolts in spruce. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



121 



2.905. Effects of reinforcing plates. The allowable concentric bearing load 
parallel to the grain for a bolt in a wood member symmetrically reinforced with bearing 
plates may be determined as follows : 

(1) Compute the L/D ratio based upon the total length of the bolt in bearing. 

(2) From figure 2-52 read the ordinate corresponding to the L/D ratio found in 
step (1). 

(3) Multiply the factor determined in step (2) by the appropriate maximum crush- 
ing strengths to obtain the allowable bearing stresses of the materials involved. 

(4) Multiply the stresses so obtained by the corresponding bearing areas to obtain 
the allowable bearing loads for each material. 

(5) The summation of these bearing loads is the allowable bearing load of the rein- 
forced member. 

The preceding method applies to plywood reinforcing plates regardless of the angle 
between the load and the face grain direction. 

The allowable concentric bearing load perpendicular to the grain can be obtained 
in a similar manner except that in step (2) figure 2-53 shall be used. 

When the load on a bolt is applied at an angle between 0° and 90° to the grain the 
allowable load may be computed by substituting in equation (2:87) the parallel and 
perpendicular bearing allowables determined by the methods outlined in the preceding 
paragraphs. 

The allowable eccentric bearing load will be one-half that obtained by the procedures 
outlined in preceding paragraphs except that in determining the concentric load, an 
allowable bearing stress higher than that of the member may be used only for the plate 
on the side on which the load is applied. 

Care must be taken that the glued area between the plate and the member is suf- 
ficient to develop the load absorbed by the plate from the bolt. 

In order to prevent splitting at the ends and edges of wood members, and also to 
prevent local crushing effects, it is recommended that cross-banded reinforcing plates be 
glued under all fittings. Cross bolts may be used to minimize splitting. 

2.906. Bushings. Bushings of light alloys or fiber materials may be used to 
increase the bearing strength of bolts. Since the possible combinations of materials for 
bolts and bushings are numerous, a specific set of allowable loads for all possible combina- 
tions cannot be given here. 

Allowable bearing loads for aluminum bushings used in combination with steel bolts 
are given by the broken curves of figures 2-48 and 2-49 for a limited number of bushing 
sizes. The diameters shown on the curves represent the outside diameters of the bushings. 
The allowable bearing loads for other sizes of aluminum bushings used in combination 
with steel bolts, and for other combinations of materials, should be determined by a 
special test or by a conservative method of interpolation with due consideration of the 
materials used. 

2.907. Hollow bolts. The use of hollow bolts with comparatively thin walls for 
bearing in wood is not recommended, as tests at the Forest Products Laboratory show 
that such bolts are little if any more efficient on a weight basis than solid bolts. When 
used, the allowable stress parallel to the grain may be obtained from N.A.C.A. Technical 
Note 296. (Ref. 2-28.) In general, tests should be made to determine the allowable 
loads at other angles to the grain. 



122 



ANC BULLETIN— DESIGN" OF WOOD AIRCRAFT STRUCTURES 



2.908 Bearing in plywood. For plywood constructed in accordance with specifi- 
cation AN-NN-P-5111) (Plywood and Veneer, Aircraft Flat Panel) or any other approxi- 
mately balanced construction (nearly equal thickness of material in both directions) 
the ultimate bearing strength of bolts loaded at any angle to the face grain corresponds 
very closely to the product of F cuw (ultimate compressive strength parallel to the face 
grain), the projected bolt area, and the L/D correction factor shown in figure 2-52. For 
appreciably unbalanced plywood constructions, use F cuw and F cux for bolts loaded at 
0° and 90° to the face grain, respectively. For loadings at other angles, use a straight- 
line interpolation. The most common use in which plywood will have to sustain bolt 
bearing loads will be as reinforcing plates on solid wood members (section 2.905). 

2.91. Glued Joints. 

2.910. Allowable stress for glued joints. 

(1) An allowable glue stress equal to one-third F su (column 14 of table 2-3) for the 
weaker species in the joint should be used for all plywood-to-plywood or plywood-to- 
solid-wood joints regardless of face grain direction and for joints between solid wood 
members in which the relative grain direction is essentially perpendicular. The reduction 
for joints in which the face grain direction of the plywood is parallel to the grain of the 
solid wood is necessary primarily because of the unequal stress distribution common 
to most plywood glue joints. 

(2) The allowable shear stress on the glue area for all joints between pieces of solid 
wood having parallel-grain gluing, is equal to the allowable shear stress parallel to the 
grain for the weaker species in the joint. This value is found in column 14 of table 2-3 
and should be used only when uniform stress distribution in the glue joint is assured. 

2.911- Laminated and spliced spars and spar flanges. Requirements for lami- 
nated and spliced spars and spar flanges are presented in ANC-19, Wood Aircraft In- 
spection and Fabrication. (Ref. 2-4. ) Provisions for limiting the location of scarf joints 
and for the required slope of grain are included. 

2.912. Glue stress between web and flange. The stress on the glue area be- 
tween web and flange may be determined by dividing the maximum shear per inch in 
plywood by the area of contact per inch. For example, the shear stress on the area of 
contact is 

f e = f ~=l (2:89) 

where : 

/ fl = shear stress on the area of contact. 

/ 5 = the maximum shear stress in the plywood. 

/ = thickness of one web. 

d = depth of the flange. 

q = shear per inch in the plywood. 

The allowable stress is determined according to section 2.910. If, for example, the 
flange were of spruce and the web were of mahogany-yellowpoplar, the allowable stress 
would be one-third the value for spruce, or 283 pounds per square inch. 

2.92. Properties of Modified Wood. It is at times desirable to impart modified 
properties to wood for reinforcement at joints, bearing plates, and for other specific uses. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



123 



Such modifications can be obtained by treating with synthetic resins, by compressing, 
or by a combination of treating and compressing. 

Investigations at the Forest Products Laboratory have produced several types of 
modified wood combinations, such as " impreg," " compreg," "semi-compreg," and " stay- 
pak," which are described in ANC Bulletin 19. When the resin is set within the structure 
by the application of heat prior to the application of assembly pressures, thus greatly 
limiting the compression of the wood, the material is called "impreg." When the treated 
wood is subjected to pressures in the range of 1,000 to 3,000 pounds per square inch 
prior to the setting of the resin, resulting in a product with a specific gravity of 1.2 to 
1.4, the material is called "compreg." Resin-treated wood with specific gravity values 
between that of impreg and compreg is known as "semi-compreg." Ordinary laminated 
wood or solid wood with no resin within the intimate structure when compressed under 
conditions that cause some flow of lignin is known as "staypak." It differs from material 
made according to conventional pressing methods in that the tendency to recover its 
original dimensions when exposed to swelling conditions has been practically eliminated. 

Some properties of parallel-laminated and cross-laminated modified wood made by 
the Forest Products Laboratory from 17 plies of J i6-inch rotary-cut yellow birch veneer 
are presented in tables 2-13 and 2-14, respectively. Average values resulting from the 
specified number of tests, together with maximum and minimum values, are given. 
Values for normal laminated wood (controls), impreg, semi-compreg, compreg, and stay- 
pak are presented. Conclusions drawn from these comparative tests must be regarded 
only as indicative, because the number of tests is limited. 

2.920. Detailed Test Data for Tables 2-13 and 2-14. Specimens for test were ob- 
tained from three sets of 24- by 24-inch panels, each made of 17 plies of X$-w.ch yellow 
birch veneer. Each set consisted of two panels of each of the five materials, one panel 
parallel-laminated and one cross-laminated. Panels of a set were formed by assembling 
corresponding plies of the panels from successive sheets of veneer as it came from the 
lathe. So far as possible, the veneer for each set was taken from a different log or bolt. 

Except as otherwise noted, tests were made on specimens with the original or formed 
surfaces of the material undisturbed. In general, an equal number of specimens was 
tested from each of the two principal grain directions, lengthwise and crosswise (0° and 
90°), namely, parallel and perpendicular, respectively, to the grain of parallel-laminated 
panels, and to the face grain of the cross-laminated panels. 

Tension parallel to grain (A, tables 2-13 and 2-14). Specimens were 1 inch wide 
by panel thickness (t) by 24 inches long, shaped to have a 2 1 2-inch long central section 
yi inch wide. The taper followed a 90-inch radius on each edge. 

Tension perpendicular to grain and parallel to laminations (B, tables 2-13 and 
2-14). Specimens were 1 inch by (t) by 16 inches long, shaped to have a 2 1 "2-inch long 
central section J 2 inch wide for table 2-13 and 3^t inch wide for table 2-14, with radii 
of 30 and 60 inches, respectively. 

Compression parallel to grain (C, tables 2-13 and 2-14) and perpendicular to grain 
and parallel to laminations (D, tables 2-13 and 2-14). Specimens were 1 inch by (t) 
by 33^ to 4 inches long for the controls; impreg and semi-compreg specimen lengths were 
approximately 4t. Compreg specimens were 1 inch by (t) by 1 inch long for maximum 
and proportional limit stresses, and 1 by (t) by 3^2 inches long for modulus-oi'-elasticity 



STRENGTH OK WOOD AND PLYWOOD ELEMENTS 



125 



Si 1 


302.9 
14.37 

4.8 


22 = 


3,990 
6,130 

367.4 


183 9 
11.60 

3.9 




4,810 
6,370 

385.2 


*M8 4 
12.72 
4.33 


33.7 
4.3 
29.4 




: ^ ^ c. c. 






5,010 
8,270 


358.8 
173.1 
6.74 
1.30 


1 




3,160 
6,780 


315.5 
136.8 
4.0 
.64 


S : 




4,070 
7,370 


333.4 
161.2 
5.40 

.97 




5 




CO O C. 






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194.9 


98.7 
1.13 

5.6 


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1.97 
7.93 


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126 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



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STRENGTH OF WOOD AND PLYWOOD ELEMENTS 




128 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



determinations. Staypak specimens were 1 inch by (t) by 2 and 4 inches long for pro- 
portional limit and modulus data, and 1 by (t) by 1 and 2 inches long for maximum stress. 

Compression perpendicular to laminations (E, tables 2-13 and 2-14). Specimens 
were 1 by 1 inch by panel thickness (t), except for compreg and staypak, which con- 
sisted of two thicknesses of material, each 1 inch square, placed one upon the other. 
Deformations were measured between the fixed and movable heads of the testing 
machine. 

Static bending (F and G, tables 2-13 and 2-14). Specimens 1 inch wide by height 
(t) were tested as a simple beam with center loading on spans ranging from 14t to 16t. 

Shear parallel to grain and perpendicular to laminations (H, table 2-13). Notched 
specimens were 2 inches by (t) by 2 1 i inches (as illustrated in figure 13 of A.S.T.M. 
specifications for tests of small clear timber specimens, Designation D143-27) with 
shearing surface 2 inches by (t). Specimens tested in the Johnson-type shear tool were 
1 inch by (t) by 3 inches (two 1-inch by (t) shearing surfaces). 

Modulus of rigidity tests (I, table 2-13 and H, table 2-14) were conducted on 
panels approximately 24 inches square by full thickness of the material, using the plate 
shear method developed by the Forest Products Laboratory for measuring the shearing 
moduli of wood, as described in Mimeograph No. 1301. 

Torsion tests (J, table 2-13 and I, table 2-14) were conducted on rectangular speci- 
mens of width 3t by thickness (t) by 16 to 24 inches long, gripped flatwise and with 
detrusion measuring device applied to their edges. Following tests on these, with 
torque kept within the proportional limit, specimens were cut to a width of 2t and the 
test repeated. 

Toughness (K, table 2-13 and J, table 2-14) specimens 5 % by (t) by 10 inches long 
with grain of parallel-laminated material and face grain of cross-laminated material 
parallel to length were tested over an 8-inch span on the Forest Products Laboratory 
toughness machine with plane of laminations parallel to direction of load. 

Impact (Izod type) specimens (L, table 2-13) had the grain lengthwise and the 
notch in an original surface. Some of the staypak specimens were less than inch 
thick, but the dimension from the base of the notch to the opposite face was standard. 

Water absorption (M, table 2-13) specimens were 1 by ? 8 by 3 inches. The grain was 
parallel to the 1-inch dimension. One face was an original surface sanded and the other 
surfaces were machined. Specimens were heated for 24 hours at 122° F., cooled, weighed, 
immersed in water at room temperature for 24 hours, and the percentage increase in 
weight during immersion calculated. 

Fabricated thickness changes (N, table 2-13). Equilibrium swelling and recovery 
from compression were determined from specimens }i inch by (t) by 2 inches long (grain 
parallel to the J s-inch dimension). Specimens were immersed in water at room tem- 
perature until equilibrium moisture content was reached, and the percentage increase 
in thickness (swelling plus recovery) calculated. The specimens were then oven-dried, 
measured, and percentage recovery and equilibrium swelling determined. 



STRENGTH OF WOOD AND PLYWOOD ELEMENTS 



129 



REFERENCE FOR CHAPTER 2 

(2-1) Elmendorf, A. 

1920. . data on the design op plywood for aircraft. N. A.C.A. Tech. Report 84. (Also 
Forest Products Laboratory Mimeo. 1302.) 

(2-2) Forest Products Laboratory 

1940. wood handbook. U. S. Dept. Agr. Unnumbered Publ. (Revised.) 

(2-3) 

1941. specific gravity-strength relations for wood. Forest Products Laboratory 
Mimeo. 1303. 

(2-4) 

1943. wood aircraft inspection and fabrication-. AXC-19. 
(2-5) Freas, A. D. 

1942. methods of computing strength and stiffness of plywood strips in bending 
Forest Products Laboratory Mimeo. 1 304. 

(2-6) Jenkin, C. F. 

1920. REPORT ON MATERIALS USED IN AIRCRAFT AND AIRCRAFT ENGINES. (Gr. Brit.) Mu- 

nitions- Aircraft Production Department. Aeronautical Research Committee. 
(2-7) Lewis, W. C. and Dawley, E. R, 

1943. stiffeners in box beams and details of design. Supplement to: Design of Ply- 
wood Webs in Box Beams. Forest Products Laboratory Mimeo. 1318A. 

1 2—8) Lewis, W. C; Heebink, T. B.; Cottlngham, W. S.; and Dawley, E. R. 

1943. buckling in shear webs of box and I-beams and the effect upon design criteria. 
Supplement to: Design of Plywood Webs in Box Beams. Forest Products Laboratory 
Mimeo. 1318 B. 
(2-9) Liska, J. A. 

1942. TENTATIVE METHOD OF CALCULATING THE STRENGTH AND MODULUS OF ELASTICITY OF 

plywood in compression. Forest Products Laboratory Mimeo. 1315. 
(2-10) Lundquist, E. E.; Kotanchik, J. N.; and Zender, G. W. 

1942. a study of the compressive strength of stiffened plywood panels. N. A.C.A. 

Advanced Tech. Note. (Restricted.) 
(2-11) March, H. W. 

1 941 . SUMMARY OF FORMULAS FOR FLAT PLATES OF PLYWOOD UNDER UNIFORM OR CONCEN- 
TRATED LOADS. Forest Products Laboratory Mimeo. 1300. (Revised. > 
(2-12) 

1942. BUCKLING OF FLAT PLY WOOD PLATES IN COMPRESSION, SHEAR, OR COMBINED COMPRES- 
SION and shear. Forest Products Laboratory Mimeo. 1316. 
(2-13) 

1942. flat plates of ply wood under uniform or concentrated loads. Forest Prod- 
ucts Laboratory Mimeo. 1312. 

(2-14) 

1943. buckling of long, thin plywood cylinders in axial compression. Forest Prod- 
ucts Laboratory Mimeo. 1322 and supplements 1322-A and 1322-B. 

(2-15) Markwardt, L. J. 

1930. aircraft woods: their properties, selection, and characteristics. N. A.C.A. 
Tech. Report 354. (Also Forest Products Laboratory Mimeo. R1079.) 
(2-16) 

1938. FORM FACTORS AND METHODS OF CALCULATING THE STRENGTH OF WOODEN BEAMS. 

Forest Products Laboratory Mimeo. R1184. 



130 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



(2-17) Markwardt, L. J., and Wilson, T. R. C. 

1935. STRENGTH AND RELATED PROPERTIES OF WOODS GROWN IN THE UNITED STATES. U. S. 

Dept. Agr. Tech. Bull. 479. 
(2-18) Xewlin, J. A. 

1939. bearing strength of wood at an angle to the grain. Engineering News Record, 
May 11, 1939. 

(2-19) 

1940. formulas for columns with side loads and eccentricity. Building Standards 
Monthly, December, 1940. 

(2-20) Newlin, .1. A., and Gahagan, J. M. 

1930. tests of large timber columns and presentation of the forest products lab- 
oratory column formula. U. S. Dept. Agr. Tech. Bull. 167. 
(2-21) Newlin, J. A., and Trayer, G. W. 

1923. form factors of beams subjected to transverse loading only. N.A.C.A. Tech. 
Report 181. (Also Forest Products Laboratory Mimeo. 1310.) 

(2-22) 

1924. stresses in wood members subjected to combined column and beam action. 
N.A.C.A. Tech. Report 188. (Also Forest Products Laboratory Mimeo. 1311.) 

(2-23) 

1930. the design of airplane wing ribs. N.A.C.A. Tech. Report 345. (Also Forest 
Products Laboratory Mimeo. 1307.) 
(2-24) Norris, C. B. 

1937. the technique of plywood. Hardwood Record, October 1937 to March 1938. 

(2-25) 

1943. the application of mohr's stress and strain circles to wood and plywood. 
Forest Products Laboratory Mimeo. 1317. 
(2-26) Norris, C. B. and McKinnon, P. F. 

1943. compression tests. Supplement to: Compression, Tension, and Shear Tests on 
Yellowpoplar Plywood Panels of Sizes that do not Buckle with Tests made at Various 
Angles to the Face Grain. Forest Products Laboratory Mimeo. 1328 A. 
(2-27) Norris, C. B. and Voss, A. W. 

1943. effective width of thin plywood plates in compression with face grain at 0° 
and 90° to load. Forest Products Laboratory Mimeo. 1316 E. 
(2-28) Trayer, G. W. 

1925. bearing strength of wood under steel aircraft bolts and washers and other 
factors influencing fitting design. N.A.C.A. Tech. Note 296. 

(2-29) 

1930. wood in aircraft construction. National Lumber Manufacturers Association. 

(2-30) 

1930. the design of plywood webs for airplane wing beams. N.A.C.A. Tech Bull. 344. 

(2-31) 

1932. the bearing strength of wood under bolts. U. S. Dept. Agr. Tech. Bull. 332. 
(2-32) Trayer, G. W., and March, H. W. 

1931. ELASTIC instability of members having sections common in aircraft construc- 
tion. N.A.C.A. Tech. Report 382. 

(2-33) Wilsox, T. R, C. 

1932. strength-moisture relations for wood. U. S. Dept. Agr. Tech. Bull. 282. 



METHODS OF STRUCTURAL ANALYSIS 



131 



CHAPTER 3. METHODS OF STRUCTURAL ANALYSIS 

TABLE OF CONTENTS 



3.0 GENERAL 133 

3.00 Purpose 133 

3.01 Special Considerations in Static Test- 
ing of Structures 133 

3.010 Element Tests 133 

3.01 1 Complete Structures 134 

3.01 10 Design Allowances for Test Condi- 
tions 134 

3.01 1 1 Test Procedure 135 

3.1 WINGS 135 

3.10 General 135 

3.11 Two-spar Wings with Independent 
Spars 135 

3.110 Spar Loadings 135 

3.111 Chord Loading 138 

3.112 Lift-truss Analysis 140 

3.1120 General 140 

3.1121 Lift Struts " 140 

3.1122 Jury Struts 143 

3.1123 Nonparallel Wires 143 

3.1124 Biplane Lift Trusses . . .' 143 

3.1125 Rigging Loads 144 

3.113 Drag-truss Analysis 144 

3.1130 Single Drag-truss Systems 144 

3.1131 Double Drag-truss Systems 145 

3. 1 1 32 Fixity of Drag Struts 1 45 

3.1133 Plywood Drag-truss Systems. . . .145 

3.1 14 Spar Shears and Moments 145 

3.1140 Beam-column effects (Secondary 
bending) 148 

3.1141 Effects of Varying Axial Load and 
Moment of Inertia 148 

3.115 Internal and Allowable Stresses for 
Spars 148 

3.1150 General 148 

3.1151 Wood Spars 149 

3.116 Special Problems in the Analysis of 
Two-spar Wings 150 

3.1 160 Lateral Buckling of Spars 150 

3.1161 Ribs 150 

3.1 162 Fabric Attachment 151 

3.12 Two-spar Plywood Covered Wings . 151 

3.120 Single Covering 151 

3.121 Box Type 151 

3.13 Reinforced Shell Wings 151 

3.130 General 151 

3.131 Computation of Loading Curves. 153 

3.1310 Loading Axis 153 

3.131 1 Loading Formulas 153 



3. 1 32 Computation < >f Shear, Bending Mo- 
ment, and Torsion 155 

3.133 Computation of Bending Stresses . 156 

3.1330 Section Properties 157 

3.1331 Bending Stress Formulas 161 

3.134 Secondary Stresses in Bending Ele- 
ments 163 

3.135 Computation of Shear Flows and 
Stresses 164 

3.1350 General 164 

3.1351 Shear Flow Absorbed by Bending 
Elements 164 

3.1352 Shear Correction for Beam Taper 167 

3.1353 Simple D Spar 167 

3.1354 Rational Shear Distribution 169 

3.13540 Single Cell— General Method. . . 169 

3.13541 Two Cell— General Method 171 

3.13542 Two-Cell Four-Flange Wing . . . 176 

3.13543 Shear Centers 179 

3.136 Ribs and Bulkheads 180 

3.1360 Normal Ribs 180 

3.13600 Rib-Crushing Loads 181 

3.1361 Bulkhead Ribs 181 

3.137 Miscellaneous Structural Problems 182 

3.1370 Additional Bending and Shear 
Stresses due to Torsion 182 

3.1371 General Instability 182 

3. 138 Strength Determination 182 

3.1380 Buckling in Skin 183 

3.1381 Compression Elements 183 

3.1382 Stiffened Panels 183 

3.1383 Tension Elements 185 

3.1384 Shear Elements 185 

3.2 FIXED TAIL SURFACES 185 

3.3 MOVABLE CONTROL SURFACES . .185 

3.4 FUSELAGES 186 

3.40 General 186 

3.41 Four-longeron Type 187 

3.42 Reinforced-shell Type 191 

3.421 Stressed-skin Fuselages 191 

3.422 Computation of Bending Stresses . 191 

3.423 Computation of Shearing Stresses 193 

3.43 Pure-shell Type 194 

3.431 Monocoque shell Fuselages 194 

3.44 Miscellaneous Fuselage Analysis 
Problems 195 

3.441 Analysis of Seams 196 

3.442 Analysis of Frames and Rings . . . .196 

3.4421 Main Frames 196 

3.4422 Intermediate Frames 198 

3.443 Effects of Cut-Outs 198 



132 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



3.444 Secondary Structures Within the 



Fuselage 198 

3.45 Strength Determination 198 

3.5 HULLS AND FLOATS 199 

3.51 Main Longitudinal Girder 199 

3.52 Bottom Plating 199 



3.53 Bottom Stringers 200 

3.54 Frames. 201 

3.55 Strength Determination 201 

3.6 MISCELLANEOUS 201 

References 203 



METHODS OF STRUCTURAL ANALYSIS 



3.0. GENERAL. 

3.00. Purpose. It is the purpose of the Methods of Structural Analysis portion 
of this bulletin to present acceptable procedures for use in determining the internal 
stresses resulting from the application of known external loads to wood and plywood 
aircraft structures. The basic design procedures that have been developed for use in 
analyzing metal structures are generally applicable to the problem of wood structures 
provided that suitable modifications are made to account for the differences in physical 
characteristics. The designer's attention is directed to existing text material covering 
the treatment of common stress-analysis problems not treated herein, and to the current 
preparation of an Army-Navy-Civil Bulletin, ANC-4 "Methods of Structural Analysis." 

It is to be emphasized that the analysis procedures described in this bulletin arc 
not presented as required procedures but represent suggested methods that are accept- 
able to the Army, Navy, and Civil Aeronautics Administration. The nature, magnitude, 
and distribution of the loads for which the airplane structure shall be designed are 
defined by the applicable specification, regulation, handbook, or bulletin of the procur- 
ing or certificating agency. 

Submission of a stress analysis, although such an analysis employs a method of 
procedure which is considered acceptable by the procuring or certificating agency, does 
not necessarily constitute satisfactory proof of adequate strength. The stress analysis 
should be supplemented by pertinent test data. Unless a structure conforms closely 
to a previously constructed type, the strength of which has been determined by test, a 
stress analysis is not considered as a sufficiently accurate and certain means of determin- 
ing its strength. Most desirable is a test of the complete structure under the critical 
design-loads. However, tests of certain component parts and of specimens employing 
generally typical construction and detail design features are of great assistance both in 
justifying allowable stresses and in proving analysis methods. In each individual case, 
the extent and nature of the structural test program required to substantiate the stress 
analysis is specified by the procuring or certificating agency. 

3.01. Special Considerations in Static Testing of Structures. Since the allow- 
able stress values given in Chapter 2, table 2-3, are based on a definite moisture content 
and method of load application, consideration should be given to these variables, both 
in using element tests to establish design allowable stresses and in designing structures 
to be statically tested as complete structures. Elements include simple structural 
members and details, such as panels, stiffened panels, or sections of spars. Complete 
structures include wing panels, center sections, fuselage, stabilizer, or other parts in- 
dividually or in combination. These two types of test will be discussed separately 
since they are treated differently. 

3.010. Element Tests. A comparison of the design values listed in table 2-3 
with the results of standard tests at 12 percent moisture content (ref. 2-17) shows 
that test results may be made approximately comparable to the design values by the 



133 



134 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



following methods. Enough tests should be made to cover variability but the required 
number will be governed by various factors as discussed in the following. 

Case A. When the type of element and the mode of failure are such that the results 
of element tests can be directly related to the physical properties of coupons cut from 
the materials used in the elements, the results of element tests may be corrected by 
the ratio of the design values in table 2-3 to the test coupon values. Care should be 
taken that the elements and the coupons are tested at a slow rate, at the same moisture 
content, and under approximately the same time-loading conditions. The test ele- 
ment should be made of matched materials; for example all stiffeners in a stiffened 
panel should be made from the same stock. 

Case B. When it is not practicable to correct element tests by means of related 
tests on coupons, the following procedure may be employed: 

(1) A sufficient number of tests should be made to establish a reasonably reliable 
average considering the variability of the materials. Fewer tests will be required and 
the scatter of related tests will be reduced if the test results are corrected to the average 
specific gravity values listed in table 2-3 by the methods of section 2.01. For the same 
reason, it is desirable to use material of approximately average specific gravity in test 
specimens. 

(2) The strength should be adjusted to 12 percent moisture by factors from table 
2-2 appropriate to the primary mode of failure. Should failure occur in glued or bolted 
fastenings, however, no upward adjustments should be made. It should be recognized 
that moisture adjustments are subject to error and should, therefore, be avoided when- 
ever possible by conditioning test specimens to approximately 12 percent moisture 
content. 

(3) In element tests it will usually be possible to arrange the test procedure so 
that errors due to rate and duration of load will be negligible in comparison with other 
experimental errors, for example: 

(a) If the maximum load is supported for 15 seconds or more, such as in tests 
where the load is added by weight increments, corrections for rate and duration of 
load are unnecessary. 

(b) If the speciment is loaded at a rate of strain such that the time from zero 
load to failure is more than 2 minutes when the testing machine is operated contin- 
uously, corrections are unnecessary. Thus, if the first stopping point is 25 percent of 
the expected ultimate load and the machine takes Yi minute to reach this load, the 
rate of strain is sufficiently low. 

The time to failure after passing the limit load should be not more than 5 minutes 
if possible (slower loading results in lower ultimate loads) since upward corrections 
of test values, because of long duration, are considered inadvisable. 

(4) After correction of the average test results for moisture, a correction factor 
to allow for variability should be applied as follows: 

(a) 0.94 when the failure is principally the result of compression, tension, or 
bending stresses, or shear in 45° plywood. 

(b) 0.80 when the failure is principally due to shear stresses parallel to the 

grain. 

3.011. Complete Structures. 

3.0110. Design Allowances for Test Conditions. When a complete structure 



METHODS OF STRUCTURAL ANALYSIS 



135 



is static tested, it is not usually possible to make the test under the conditions on which 
the design values of table 2-3 are based. Therefore, if the purpose of the test is to prove 
the strength of the entire structure at a specified ultimate load regardless of test con- 
ditions (which is usually the case in order to prove joints and fittings) it is recommended 
that the designer investigate the effects of probable test conditions prior to designing 
the structure on the basis of table 2-3. 

If it appears that the probable test conditions will cause the strength in the test 
to be less than that corresponding to design values in table 2-3, suitable margins of 
safety should be incorporated during the design. 

3.0111. Test Procedure. In complex composite structures the effects of moisture 
content on over-all strength are uncertain. Changes in wood strength may be offset 
by stress concentration effects. It is, therefore, desirable that complete structures be 
conditioned as closely as possible to 12 percent moisture content at the time of testing. 

To minimize effects of rate and duration of load, the time to failure after passing 
limit load should be less than 15 minutes if possible. 

The ultimate load should be sustained without failure for at least 15 seconds, in 
order to insure the test being comparable to design values in regard to time effects. 

The above procedure may be varied depending upon the purpose of the test. Agree- 
ment should be reached with the procuring or certificating agency regarding the test 
procedures and methods of correction, if any, prior to conducting major tests. 

3.1. WINGS. 

3.10. General. Because of the basic differences in their structural behavior, 
separate stress analysis procedures are outlined for the following general types of wing 
structures : 

(a) Two-spar wings with independent spars. 

(b) Reinforced shell wings. 

3.11. Two-Spar Wings with Independent Spars. The methods of analysis pre- 
sented under this heading are based on the assumption that the spars deflect inde- 
pendently in bending. Such methods are particularly applicable to two-spar fabric- 
covered wings with drag bracing in a single plane. They may also be applied to two- 
spar wings having drag bracing in two planes. In such cases, the effect of the torsional 
rigidity resulting from the double drag bracing, tending to equalize the deflections of 
the two spars, is usually neglected but may be taken into account by the methods of 
reference 3-7. 

3.110. Spar loadings. The following method of determining the running loads 
on the spars has been developed to simplify the calculations required and to provide 
for certain features which cannot be accounted for in a less general method. It is 
equivalent to assuming that the resultant air and inertia loads at each section are divided 
between the spars as though the ribs were simple beams and the spars furnished the 
reactions. Frequently, certain items are constant over the span; then the computations 
are considerably simplified. 

The net running load on each spar, in pounds per inch run, can be obtained from 
the following equations : 




(3:1) 



136 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



Vr= \{C N (a-f) - C Ma } q+>he iH) 



C 



1446 



(3:2) 



where : 

y/ = net running load on front spar, in pounds per inch 
y r = net running load on rear spar, in pounds per inch 

a > °> /> 3> an d T are shown in figure 3-1 and are all expressed as fractions of the chord 
at the station in question. The value of a must agree with the value on which C M a 

is based. 

q = dynamic pressure for the condition being investigated. 

Cm and C u a are the airfoil normal force and moment coefficients, respectively, at 
the section in question. 

C is the wing chord, in inches. 

e is the average unit weight of the wing, in pounds per square foot, over the chord 
at the station in question. It should be computed or estimated for each area included 
between the wing stations investigated, unless the unit wing weight is substantially 
constant, in which case a constant value may be assumed. By properly correlating the 
values of e and j, the effects of local weights, such as fuel tanks and nacelles, can be 
directly accounted for. 

n 2 is the net limit-load factor representing the inertia effect of the whole airplane 
acting at the center of gravity. The inertia load always acts in a direction opposite 
to the net air load. For positively accelerated conditions n% will always be negative, and 
vice versa. Its value and sign are obtained in the balancing of the airplane. 




Figure 3—1. — Unit section of a conventional 2-spar wing. All vectors are shown in positive sense. 



If it is desired to compute the airloading and inertia loadings separately, formulas 
(3:1) and (3:2) may be modified by omitting terms containing « 2 for the airloading, and 
omitting terms containing q for the inertia loading. Then the inertia loading, shear, 
and moment curves need be computed for only one condition (say, n 2 = 1.0), the values 
for any other condition being obtained by multiplying by the proper load factor. 



METHODS OF STRUCTURAL ANALYSIS 



137 



The computations required in using the preceding method are outlined in tables 
3-1 and 3-2, in a form which is convenient for making calculations and for checking. 

Table 3-1. — Computation of net unit loadings (constants) 
Stations Along Span 



1 


Distance from root, inches 


2 


C'/l44 - (chord in inches) /144 


S 


f , fraction of chord 


4 


j. n ti M 


5 


b - r - f -<3)-(D 


6 


a, fraction of chord (a.c.) 


7 


i, ' 


8 


e ■ unit wing wt., lbs/sq.ft.* 


9 


r - a =0-® 


10 


a - f «dMD 


11 


r - j -0-(7) 


12 


i - f -®-(D 


15 


C/144 b =®/(f) 



* Those values will depend on the amount of disposable 
load carried in the wing. 

The following modifications and notes apply to tables 3-1 and 3-2: 

(a) When the curvature of the wing tip prevents the spars from extending to the 
extreme tip of the wing, the effect of the tip loads on the spar can easily be accounted 
for by extending the spars to the extreme span as hypothetical members. In such cases, 
the dimension / will become negative, as the leading edge will lie behind the hypothetical 
front spar. 

(b) The local values of C N , item 14, are determined from the design values of C N 
in accordance with the proper span-distribution curve. 

(c) Item 15 provides for a variation in the local value of Cm- When a design value 
of center-of-pressure coefficient is specified, the value of Cm should be determined by 
the following equation, using item numbers from tables 3-1 and 3-2. 

C', /o =©[©-rP'] (3:3) 

(d) When conditions with deflected flaps are investigated, the value of Cm q over 
the flap portion should be properly modified. For most conditions, C M<1 will have a 
constant value over the span. 



138 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



Table 3-2. — Computation of net unit loading* (variables) 

CONDITION 



q 


°»l(»to) 




C« or C.P1 
at 



















(Refer also to Table 3-4) 



Cjj^ " (variatior. with span) 
Cj^ (variation irtth span) 



© * © 

© * © 

© x q 

Be X ® x @ 

@ * © 

y f - (20) x ©) , lbs/lnoh 



Distanoe b from root 



© x (g) 

© - © 

(23) x q 

x ® x @ 

© * @ 

y - (26) x (lo) , lba/lnoh 



C c (variation nrlth span) 
© X q 

© * ® 

y « (3l) x ©» Ib./laoh 



(e) The gross running loads on the wing structure can be obtained by assuming 
e to be zero; then, items ©, ®, and ® become zero, y f becomes © X®, y r becomes 
® X @, and y c becomes ® X ©. 

3.111. Chord loading. The net chord loading, in pounds per inch run, can be 
determined from the following equation : 

[C c q+n x2 fi\ C 



Vc=- 



144 



(3:4) 



where : 

y c = running chord load, in pounds per inch. 

C c = airfoil chord force coefficient at each station. The proper sign should be retained 
throughout t he computations. 

n T 2 = net limit chord-load factor approximately representing the inertia effect of the 
whole airplane in the chord direction. The value and sign are obtained in the balancing 
of the airplane. When C c is negative, n x i will be positive. 



140 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



q, e, and C are the same as in section 3.110. 

The computations for obtaining the chord load are outlined in table 3-2, items 28 
to 32. The following points should be noted : 

(a) The value of C c , item 28, usually can be assumed to be constant over the span. 
The only variation required is in the case of partial-span wing flaps or similar devices. 

(6) The relative location of the wing spars and drag truss will affect the drag-truss 
loading produced by the chord and normal air forces. This can easily be accounted for by 
correcting the value of C c . (Sec. 3.1121). 

It is often necessary to consider the local loads produced by the propeller thrust 
and by the drag of items attached to the wing. The drag of nacelles built into the wing is 
usually so small that it safely can be neglected. The drag of independent nacelles and that 
of wing-tip floats can be computed by using a rational drag coefficient or drag area in 
conjunction with the design speed. In general, the effects of nacelles or floats can be com- 
puted separately and added to the loads obtained in the design conditions. 

3.112. Lift-truss analysis. 

3.1120. General. In considering a lift-truss system for either a monoplane or 
a biplane and, in the subsequent investigation of the drag-truss system, due attention 
should be given to all the force components which will be applied to the attachment 
points by the lift truss. 

3.1121. Lift struts. Consider the strut-braced monoplane wing shown in figure 
3-2. The spars in the figure are shown perpendicular to the basic wing chord (the 
reference line for normal and chord loads is the M.A.C. of the wing). If the spars are 
not perpendicular to the chord reference line, the resultant of the chord and normal 
loads should be resolved into components parallel and normal to the spar, as shown in 
figure 3-3a. Also, in the general case, the drag truss will not be perpendicular to the spar 
face. This angularity should be considered (fig. 3-3b), unless it is of small order, which 
would result in a negligible correction. 

The vertical reactions on the front and rear spars from the lift struts may be de- 
termined by taking moments about point C (fig. 3-2) of all the external loads on the 

M, f Mr 

spars (sec. 3.114). Then R,= ; and R r = , where M,. f and M rr are the moments 

g 

about the spar-root attachment, point C, of the front and rear spars, respectively. 

The strut and spar axial loads may be determined by graphical or analytical methods 
on the basis of the truss A B C, if the fitting is eccentric to the neutral axis of the spar. 
If the graphical method is used, the correction for angularity of the strut to the V-H 
plane should not be overlooked. 

The strut loads also can be determined by the following formula, which includes the 
correction for angularity: 

i M true length ,„ _ N 

Strut load =-rX ^—rjl #1, v u i ^ 3:5 ^ 

n projected length in V-H plane 

After the loads in the struts have been determined, the axial load in each spar is: 
(strut load) X (—). and the chord component acting on the wing from each strut is: 
D 

(strut load ) X (— ) 



METHODS OF STRUCTURAL ANALYSIS 



141 




(a) DRAG TRUSS PERPENDICULAR TO SPAR FACE 




C'<! 

(b) DRAG TRUSS NOT PERPENDICULAR TO SPAR FACE 

Figure 3-3. — Resolution of forces into components acting on spars and drag truss. 



142 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




METHODS OF STRUCTURAL ANALYSIS 



143 



When an eccentricity, e, in the root fitting exists, the chord loads and reactions will 
act in a plane which generally is not parallel to the line AC. The effect of the eccentricity 
is to modify the vertical reactions at the strut point and root. The increment of reaction 

R h e 

to be added or subtracted is: AR = — - (fig. 3-4d). Then, the total vertical reaction 



component at the strut point is R + AR. It is, at once, apparent that the value of the 
drag-truss reaction, R h , is a function of the strut load (fig. 3-4c); therefore, if extreme 
accuracy is desired, it becomes necessary to solve for the reactions on the lift and drag 
truss by means of simultaneous equations which include expressions for all the unknowns 
involved. The reactions may also be determined by trial and error with comparable 
results if sufficient trials are made. However, unless the value of AR is in excess of 2 
percent of R, it is considered satisfactory to assume that the total reaction is R+ AR. 

3.1 122. Jury struts. In computing the compressive strength of lift struts which are 
braced by a jury strut attached to the wing, it is usually satisfactory to assume that a 
pin-ended joint exists in the lift strut at the point of attachment of the jury strut. The 
jury strut itself should be investigated for loads imposed by the deflection of the main 
wing structure. An approximate solution based on relative deflections is satisfactory, 
if the jury strut is conservatively designed to withstand vibration of the lift strut. 
When the jury strut is considered as a point of support in the wing-spar analysis, rational 
analysis of the entire structure should be made. (ref. 3-17). 

3.1123. Nonparallel wires. When two or more wires are attached to a common 
point on the wing, but are not parallel, the distribution of load between the wires may be 
determined by least work or equivalent methods. The following approximate equations 
may be used for determining the load distribution between wires, provided the loads so 
obtained are increased 25 per cent. 



B =beam component of load to be carried at the joint. 
P { =load in wire 1. 
P2 = load in wire 2. 

Vi= vertical length component of wire 1. 

V 2 = vertical length component of wire 2. 

A i and A 2 represent the areas of the respective wires. 

Li and L 2 represent the lengths of the respective wires. 

The chord components of the air loads and the unbalanced chord components of 
the loads in interplane struts and lift wires at their point of attachment to the wing should 
then be assumed to be carried entirely by the internal drag truss. 

3.1124. Biplane lift trusses. In biplanes that have two complete lift-truss and 
drag-truss systems interconnected by an N strut, a twisting moment applied to the wing 
cellule will be resisted in an indeterminate manner, as each pair of trusses can supply a 




(3:6) 




(3:7) 



where : 



144 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



resisting couple. An exact solution involving the method of least work, or a similar 
method, can be used to determine the load distribution (ref. 3-16). For simplicity, 
however, it may be assumed first that all the external normal loads and torsional forces 
about the aerodynamic center of the cellule are resisted by the lift trusses. This as- 
sumption is usually conservative for the lift trusses, but does not adequately cover the 
possible loading conditions for the drag trusses. A second condition should therefore be 
investigated by assuming that a relatively large portion (approximately 75 percent) 
of the torsional forces about the aerodynamic center of the cellule are resisted by the drag 
trusses. In the case of a singlo-lift-truss biplane, the drag trusses must, of course, resist 
the entire moment of the air forces with respect to the plane of the lift truss. 

3.1125. Rigging loads. Wire-braced structures should be designed for the 
rigging loads specified by the procuring or certificating agency. Sometimes it may 
be necessary to combine the rigging loads with internal loads from flight or landing 
conditions. 

The effects of initial rigging loads on the final internal loads are difficult to pre- 
dict, but, in certain cases, may be serious enough to warrant some investigation. In 
this connection, methods based on least work or deflection theory offer the only exact 
solution. Approximate methods, however, are satisfactory if based on rational as- 
sumptions. As an example, if a certain counter-wire will not become slack before the 
ultimate load is reached, the analysis can be conducted by assuming that the wire is 
replaced by a force acting in addition to the external air forces. The residual load from 
the counterwire can be assumed to be a certain percentage of the rated load and will, 
of course, be less than the initial rigging load. 

3.113. Drag-truss analysis. 

3.1130. Single drag-truss systems. Single drag-truss systems are employed 

in strut- or wire-braced wings where the ratio of the span of the overhang to the mean 
chord is not excessive. The requirements of the specific agency involved should be 
reviewed in regard to the upper limit on this value above which double-drag bracing 
is required. 

An example of a conventional drag truss is shown in figure 3-4 for a strut-braced 
monoplane wing. The chord loading, C, in pounds per inch run (fig. 3-4 (a)) may be 
distributed to the panel points of the truss (b) as concentrated loads 1, 2, 3, 4, etc. In 
addition to the chord loads due to air load, the lift struts also apply loads in the chord 
plane. In section 3.1121, the method of determining the chord components was given. 
These components are shown in figure 3-4 (c), assuming that the wing is so loaded 
that the lift struts are subjected to tensile loads. If items of concentrated weight, such 
as fuel tanks and landing gear, were not accounted for when the running chord load 
was computed in table 3-2, the resultant inertia loads from these items of weight should 
be applied to the drag truss. In figure 3-4 (d) are shown all the loads and reactions 
acting on the drag truss. 

The loads in the drag-truss members may now be determined by graphical or 
analytical methods. Exact division of the drag reaction, R D , on the truss is generally 
indeterminate, insofar as the front and rear root-spar attachments are concerned. In 
general, overlapping assumptions should be made, or the drag reaction conservatively 
assumed to be resisted entirely by one root fitting. Occasionally, the drag reaction 
may be divided equally between the front and rear root-spar fittings if they have ap- 



METHODS OF STRUCTURAL ANALYSIS 



145 



proximately the same rigidity in the drag direction. 

3.1131. Double drag-truss systems. A double drag truss is employed in canti- 
lever wings or braced wings where it is necessary to provide additional torsional rigidity 
outboard of the strut point. The investigation of double-drag trusses follows the same 
line of procedure outlined in section 3.1130. The design of the double truss is usually 
dictated by torsional rigidity requirements rather than by the actual design loads 
applied to the structure. 

In showing compliance with requirements in which the upper drag wire in one 
bay and the lower drag wire in the adjacent bay are assumed in action (the remaining 
wires in these two bays assumed to be out of action), the loads on the strut take the 
form shown in figure 3-5. R wu and A',,,; represent the wire force components along the 
drag strut. In general, it will be necessary to balance these components in the drag 
direction by a reaction, R w i — R wu \ then, taking moments about a convenient point, 
the vertical couple force R c may be determined. Having the forces and reactions on 
the drag strut, the internal forces readily may be determined. 

[ Compon ents Along Drag Strut 
"[Emm Wires 




V 

Se ction A- A 

Figure 3-5. — Double drag truss — two drag; wires in action. 

3.1132. Fixity of drag struts. Drag struts should be assumed to have an end-fixity 
coefficient of 1.0, except in cases of unusually rigid restraint, in which a coefficient 
of 1.5 may be used. 

3.1133. Plywood drag-truss systems. In a two-spar, plywood-covered wing, 
the plywood covering, together with the drag struts, is usually depended upon to carry 
the chord shear. Section 3.12 gives methods of analysis of this type of structure. 

3.114. Spar shears and moments. The fundamental principles of statics should 
be employed in the determination of wing-spar shears and bending moments. Before 
proceeding with the detailed determination of these items, it is essential, in order to 
avoid errors, that all the external loads and reactions be determined for the spar. 

The primary bending moments at various stations on a cantilever spar may be 



146 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



determined conveniently by the equation : 

M x =M 1 ±Six£ 



Fa 



(3:8) 



where Mi and S x are the moment and shear at station 1 ; x, the distance between station 
1 and x; and > Fa, the sum of the moments about station x of all the loads acting 
between the stations. It will be found desirable to prepare a table similar to the one 
shown in figure 3-6 to facilitate the computations. If the distances between the var- 
ious stations are relatively small, the center of gravities, a, of the trapezoidal loadings 



f ' 














1 


"1 


» n 


2 ( 




n 




/ 
/ 














d l — » 


*a3-» 


d 2-^ 




d 3 -^ 


<-»!-» 


d4 , 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


Section 


Distance 
from 
Root 


Distance 
between 
Sections 
d 


Load 
per in. 

w 


Average 
load 
per in. 
w a 


Load 
between 

Sections 
F 


Arm to 
centroid 
(1)* 
a 


Moment 
11' • Fa 


Shear 
S - £F 


Moment 
H" • Sd 


Moment 

at 
Section 


4 


d 4 




w 4 






















d 4 - dj 




w 4* w 3 

2 


Item ® 

X 

Item (|) 


(1)* 
■l 


(2)* 
F4-3 
x a} "*~ 






U 


3 


d 5 




w 3 










F 4 -3 


< 








d 3 -d 2 




Wj+Wg 

2 


Item © 

X 

Item (5) 


a 2 


F3-2 




(3)» 
S3 X 
(d s -d 2 ) 




2 


dg 




w 2 










F 4-3+ 
F 3-2 










d 2 -d x 




w 2* w l 

2 


Item (3) 

X 

Item © 


a 3 


F2-1 
x a 3 








1 


d l 




w l 










F 4-3 + 
F3-2 ♦ 
F2-1 














"0 














1 



NOTES 

(1) The center of gravity of a trapezoidal loading may be determined by the formula x = 2+R 

e 3(1*R) 

where R ■ h2 ; then a\ - x(d 4 -dj) 
h x 



(3) Sj, Sg etc. is shear at stations 3, 2, etc. (Item 9) 



T 

h 2 


; 


: 


T 


1 


















c 





Figure 3-6. — Determination of shears and bending moments. 



METHODS OF STRUCTURAL ANALYSIS 



147 




(«) BINDING MOMENT and SHEAR DIAORAM - CAHTHEVZR gPAR 




STRUT LOAD » v 




Figure 3-7. — (a) Bending moment and shear diagram — cantilever spar, (b) Bending moment and shear 

diagram — braced spar. 



148 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



may be assumed to lie midway between the stations with negligible error and slightly 
conservative results. If concentrated loads exist at points on the span, the table may 
be modified easily to account for these loads. 

The case of an externally braced spar may be handled in a manner similar to that 
for the cantilever spar, insofar as the determination of the shears and moments out- 
board of the strut and the moment at the root due to external loads are concerned. 
The root moment required in section 3.121 to determine the lift-strut reactions may be 
obtained conveniently by the foregoing procedure. 

The general form of the moment and shear curves is shown in figure 3-7, (a) and 
(6), for braced and cantilever spars. It always is desirable to plot the bending moment 
and shear curves as a general check of the computations and to facilitate the investi- 
gation of stations along the span not covered in figure 3-6. 

3.1140. Beam-column effects. (Secondary bending). In connection with the 
bending moment and shear curves for a braced spar inboard of the strut point, where the 
spar is loaded as a beam and a column simultaneously, the effects of secondary bending 
should be taken into account by use of the "precise" equations or the "polar diagram" 
method. The solution of the beam-column problem is covered extensively in several 
textbooks relative to airplane structures, and, therefore, will not be covered here (refs. 
3-1, 3-15). It is necessary, however, to base such computations on ultimate loads rather 
than on limit loads, in order to maintain the required factor of safety. Continuous 
spars having three or more supports should be investigated by means of the three- 
moment equation or other methods leading to equivalent results. 

3.1141. Effects of varying axial load and moment of inertia. The drag-truss bays 
of a braced wing usually are shorter than the lift-truss bay, as indicated in figure 3-4. 
The axial loads in the spars due to the chord loading, therefore, vary along the span. 
Although the "precise" equations for a beam-column assume a constant value of axial 
load in the beam, it is generally satisfactory to determine a weighted value of axial 
load for use in determining the "precise" bending moment . Referring to figure 3-8: 

U _1 J \ Li + Po L2+P3 L3 

' - L^U+U < (3:9) 

where P c is the weighted axial load due to chord loading, and P h P%, and P 3 are the spar 
axial loads in the drag bays 1, 2, and 3. The total axial load in the spar is : 

p,=p s + p c (3:10) 

where P s is the spar axial-load component from the lift strut or wire. 

Generally, the moment of inertia, I, also varies along the span and a weighted value 
of / may be determined for use in the "precise" equations, as follows: 

T _1 1 L\-\-p2 L2+/3 L3 . 

where 1 1, 1 2, and 7 3 are the moments of inertia in bays 1, 2, and 3. If the " polar diagram" 
method is used, the actual variation can be taken into account. 
3.115. Internal and allowable stresses for spars. 

3.1150. General. The allowable stresses for spars may be found in section 2.3. 
In beams subjected to combined bending and compression, the margin of safety computed 



METHODS OF STRUCTURAL ANALYSIS 



149 



r 











W-lb.per In. 






















< 


< L 2 > 


, L 5 > 



Figure 3-8. — Distribution of forces on wood spar section. 



by a simple comparison of the internal and allowable stresses may be meaningless, 
particularly when the beam-column is approaching the critical buckling point. True 
margins of safety may, therefore, be determined only by successive approximations. 
For example, if a spar is rechecked after increasing all external loads and moments by 
10 per cent, and still found satisfactory, the true margin of safety is at least 10 per cent. 

3.1151. Wood spars. In general, a spar will be subject to bending, axial (tension 
or compression), and shear stresses. The total stress due to bending and axial load may 
be computed by the usual expression: 

f,=^+| ,3:12, 



where M includes secondary bending. In computing the section properties of a wood 
spar, the following points are worthy of attention. Consider the spar section shown 
in figure 3-9. 

(a) Where the two vertical faces of the spar are of different depths, the average 
depth of the section may be used, as shown by h. 

(b) If the webs are plywood, only those plies parallel to the spar axis and one- 
quarter of those plies at 45° may be used in the computation of A and / of the sections. 
These are approximate rules to allow for the difference in modulus of elasticity of the ply- 
wood and the solid wood. If the plywood webs are neglected entirely, the computation 
of the section properties is simplified and the results are more conservative. 

(c) When investigating a section, such as A— A in figure 3-9, the full section should 
be considered effective only if the glue area is sufficient to develop the full strength of 
the side plates. In general, the distance a should not be less than 10 times or 15 times 
the thickness of a side plate for softwoods and hardwoods, respectively. The reinforcing 
blocks should be beveled, as shown, to prevent stress concentration which may lead to 
consequent failure in the glued joint at the edge of the reinforcement. 

(d) Filler blocks may likewise be used in computing the section properties, provided 
the length of the blocks and their glue area to webs and flanges is sufficient to develop the 
required bending stresses. 

(e) In the detailed investigation of a spar section, the reduction in strength due to 
bolt holes should be considered when computing the section properties. In computing 



t 



150 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



the area, moment of inertia, etc., of wood spars pierced by bolts, the diameter of the bolt 
hole should be assumed greater than the actual diameter by the amount specified by the 
procuring or certificating agency. In computing the properties of section A-A (fig. 3-9), 
it should be assumed that all the bolt holes pass through the section, because failure 
might actually occur along the line u-v. 




Section A-A 



SOLID SPAR 

Figure 3-9. — Wood spar section. 



The longitudinal shear stress in the web of a spar may be obtained from the ex- 
pression : 

SQ 



b'l 



(3:13) 



In the determination of Q, for spars with plywood webs, the recommendations in (6) 
should be followed. However, the value of b' in the expression should be the total web 
thickness. For tapered spars, the shear stress may be reduced to allow for the effects 
of taper in accordance with section 3.1352. 

3.116. Special problems in the analysis of two-spar wings. 

3.1 160. Lateral buckling of spars. For conventional two-spar wings, the strength 
of the spars against lateral buckling may be determined by considering the sum of 
the axial loads in both spars to be resisted by the spars acting together. The total 
allowable column strength of both spars is the sum of the column strengths of each spar 
acting as a column the length of a drag bay. Fabric wing covering may be assumed to 
increase the fixity coefficient to 1.5. When further stiffened by plywood or metal lead- 
ing-edge covering extending over both surfaces forward of the front spar, the fixity coeffi- 
cient may be assumed to be 3.0. 

3.1 161. Ribs. Analytical investigation of a rib generally is not acceptable as proof 
of the structure. In some cases, however, a rib may be substantiated by analysis when 
another rib of similar design has been analyzed, and subsequently strength-tested. In 



METHODS OF STRUCTURAL ANALYSIS 



151 



general, it may be desirable to analyze a rib in order to determine the approximate 
sizes of the members. 

3.1162. Fabric attachment. Although the fabric-attaching method usually is not 
stress analyzed, it is, of course, important that the rib-lacing strength and spacing 
be such that the load will be adequately transmitted to the ribs. The specifications of the 
procurement or certificating agency in regard to lacing-cord strength and spacing should 
be followed. Unconventional fabric-attachment methods should be substantiated by 
static tests or equivalent means to the satisfaction of the agency involved. 

3.12. Two-spar Plywood Covered Wings. 

3.120. Single covering. Two-spar wings covered with plywood on only one surface 
(upper or lower) should be considered as independent spar wings, in accordance with 
section 3.11, and the plywood covering designed to carry the chordwise sheer loads with 
the ribs functioning as stiffeners and load distribution members. The center of shear 
resistance of the plywood covering may be eccentric to the applied drag load (fig. 3-15 b). 
The resulting torque will then be resisted by a couple consisting of up-and-down forces 
on the two spars. 

3.12 1. Box type. Two-spar wings with both upper and lower surfaces covered with 
plywood, forming a closed box, should be treated as shell wings in accordance with section 
3.13. 

3.13. Reinforced Shell Wings. 

3.130. General. The types of wing structure considered under this heading are 
those in which the outside covering or skin, together with any supporting stiffeners, 
resists a substantial portion of the wing torsion and some of the bending. Various types 
of shell wings may be classified according to: the number of vertical shear webs, or 
number of "cells" into which these webs divide the wing section; whether the span wise 
material is concentrated mainly at the shear webs or distributed around the periphery 
of the section- as longitudinal stiffeners; whether the skin is "thin" so that it buckles 
appreciably at ultimate load, or "thick" so that it does not buckle appreciably. Typical 
shell wing sections are shown in figure 3-10. 

In shell wings the distributed airloads normal to the surface are carried to the ribs 
by the skin and its stiffeners. The ribs maintain the shape of the section and transmit 
the airloads from the skin to the vertical shear webs or to other portions of the skin 
such as the leading edge, which are capable of carrying vertical shear. Main or "bulk- 
head" ribs perform similar functions for concentrated loads, such as those due to nacelle 
landing gear, and fuselage reactions. The vertical shear from the ribs is carried to the 
wing reaction points by the shear webs and portions of the skin. The shear in these ele- 
ments creates axial bending stresses in the beam flange material. When comparatively 
stiff spanwise stiffeners are used, they also act as effective flange material, receiving their 
axial loads from the webs through shear in the skin. The contribution of the skin to the 
bending strength of the wing depends on its degree of buckling and relative modulus of 
elasticity. 

From this general picture, it is evident that broad simplifying assumptions are 
necessary to make a stress analysis of a shell wing practicable, and that the computed 
stresses in the various elements are likely to be less exact than in the case of statically 
determinate independent spar wings. In metal shell structures, elements which become 
too highly stressed generally yield without difficulty and the load is redistributed to less 



152 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



SINGLE CELL SECTIONS 




MULTI-CELL SECTION 



Note: Other types of Two Cell Wing Sections may have stiffeners. 
or thick skin similar to the single cells shown above. 

Figure 3-10. — Typical shell wing sections. 



METHODS OF STRUCTURAL ANALYSIS 



153 



highly stressed elements. In wood structures, however, some types of elements are un- 
able to accommodate themselves to secondary stresses which would be of no importance 
in metal structures, for example, buckles of sharp curvature relative to the thickness 
are apt to split plywood. The stress analysis methods presented in this section should 
therefore be considered only as reasonable approximations until the designer has had 
experience in applying a particular method to a particular type of structure and has 
correlated the analysis procedures with the results of static tests. 
3.131. Computation of loading curves. 

3.1310. Loading axis. In determining the shear and bending stresses in shell 
wings, it has been found convenient to transfer the distributed air and inertia loads 
to a suitable spanwise loading axis by computing net beam, chord, and torque load- 
ings at points or stations along such axis. The position of the loading axis may be 
chosen arbitrarily if the corresponding moment and torque components acting at a 
particular section of the wing are then properly applied to the various elements of the 
section in a manner consistent with their structural behavior. Since a reinforced shell 
wing is usually a complex nonisotropic structure in which some of the elements resist 
axial loads in a particular direction only, the true stress conditions resulting from the 
interaction of elements having various directions at a given section are often difficult 
to analyze. It is therefore recommended that the loading axis be located inside the 
wing, approximately parallel to the principal bending and shear elements. Such a loca- 
tion should tend to reduce errors in the process of transferring external loads and torques 
to the loading axis and redistributing them to the structural elements. Section 3.135 
shows that the use of a loading axis in the main shear web is often convenient for the 
shear distribution analysis, without further transfer of loads and torques. 

If the loading axis is located as suggested, it is necessary for it to change direc- 
tion where the principal structural elements change direction; for example, where an 
outer wing panel having dihedral or sweepback joins a straight center section. The 
loadings due to the air and inertia loads are computed for each segment of the axis 
in the usual manner, but at the point of direction change, the total moments and torque 
from the outboard segment should be resolved into the proper components relative 
to the inboard segment. 

The formulas given in section 3.1311 for computing the running loads and torque 
at various stations on the loading axis use airfoil moment coefficients (or center of 
pressure locations) based on airfoil sections parallel to the airflow. For a loading axis 
which is not perpendicular to such sections, these equations will therefore give small 
errors in the bending moment and torque values. These errors may be neglected unless 
the angle of inclination of the loading axis is large. 

3.1311. Loading formulas. The net running load at points along the loading 
axis and the net running torsion about these points may be found from the following 
equations : 



C 

yb = (C N q + n 2 e) — 



(3:14) 




(3:15) 



154 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



m« = [ \C N (x-a) + C_y a } q+n 2 e (x-j)J ^ (3:16) 
where : 

ijb = running beam load in pounds per inch of span. 
y c = running chord loads in pounds per inch of span, 
m, = running torsion load in inch-pounds per inch of span, 
a, j, and x are expressed as fractions of the chord at the station in question and locate 
points on figure 3-11 as follows: 

a locates the point in the airfoil on which the moment coefficient, CW , is based. 
j locates the resultant wing dead weight at the station. 
x is the distance from the leading edge to the loading axis, at the station. 
q = dynamic pressure for the condition being investigated. 

C N and CWo are the airfoil normal and moment coefficients at the section in question. 
C c = airfoil chord coefficient at each station. The proper sign should be retained 
throughout the computations. 

C"=the wing chord, in inches. 

e = the average unit weight of the wing, in pounds per square foot, over the chord 
at the station in question. It should be computed or estimated for each area included 
between the wing stations investigated, unless the unit wing weight is substantially 
constant, in which case a constant value may be assumed. By properly correlating the 
values of e and j, the effects of local weights, such as fuel tanks and nacelles, can be 
accounted for directly. 

n2=the net limit load factor representing the inertia effect of the whole airplane 
acting at the center of gravity. The inertia load always acts in a direction opposite to 
the net air load. For positively accelerated conditions n% will always be. negative, and vice 
versa. Its value and sign are obtained in the airplane balancing process. 

n r 2 = net limit chord-load factor approximately representing the inertia effect of 




All Vectors Are Shown in Positive Sense 



Figure 3-11. — Section showing location of load axis. 



i 



METHODS OF STRUCTURAL ANALYSIS 



155 



the whole airplane in the chord direction. The value and sign are obtained in the air- 
plane balancing process. Note that, when C c is negative, 7i x2 will be positive. 

Positive directions for all quantities are shown in figure 3-11. The computations 
required for this form of analysis can be carried out conveniently through the use of 
tables similar to tables 3-3 and 3 4. 

Table 3-3. — Computation oj net loadings (constants) 

Stations Along Span 

1 Distance from root, inches 

2 C/144 - (chord in inches) /14A 

3 x, fraction of chord 

4 a, fraction of chord (a.o.) 

5 j, fraction of chord* 

6 e » unit wing wt. , lbs/ sq.ft.* 

7 x - a -d)-.(4) 

8 x-j-(D-(D 

9 iSlZ 

144 



* These values will depend on the amount of disposable 
load carried in the wing. 

The values of yb, y c , and m t should be plotted against the span, and, in case irregu- 
larities are found, they should be checked before proceeding with the calculations. 

It is sometimes desirable to compute the airloadings and inertia loadings separately. 
The inertia loading, shear, moment and torsion curves then need be computed for only 
one condition (say, rig = 1.0), the values for any other condition being obtained by 
multiplying by the proper load factor. The foregoing formulas may be modified for 
this purpose by omitting terms containing n 3 for the airloading, and omitting terms 
containing q for the inertia loading. 

3.132. Computation of shear, bending moment and torsion. The summation of 
the areas under the loading curves determined by the method described in section 3.131, 
from the tip to any wing station will give the values of the total load (shear) and of 
the total torque (torsion) acting at the station. 

It is advisable to plot curves of the shear and torsion values against the span to 
determine if any irregularities have occurred in the computations. If concentrated 
weight and load items were not accounted for in the loading computations, they should 
be taken care of by additional computations, and their effects shown on the shear and 
torsion curves. 

The bending moments at any station of the wing can be found either by computing 
the moments, about the station, of the areas under the loading curves outboard of the 
station, taking into consideration moments due to concentrated loads, if such are present; 



156 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



Table 3-4. — Computation o] net loadings (variables) 

COHDITIOH 



q 


\(etc) 








\ 





















Distance b from root 






(Refer also to Table 3-2) 














Normal Load 


10 
U. 
12 
13 
14 


C™ (variation with span) 

c tfl - © x q 

@ * © 

7b - ©x© lba./in. 














Chord Load 


15 
16 
17 

18 
19 


c' c (variation with span) 
C'fjq - © X q 

© ♦ © 

y - ©>© lbs./in. 














Unit Torque 


20 
21 
22 
23 
24 
25 
26 


(variation with span 

© x © 

© + (§) 
(22) x q 

© x © 

@ ♦ @ 
H - © X© 















or by summing up the areas under the shear curves from the tip to the station. A con- 
venient tabular method of computing these values is also shown in figure 3-6; and 
typical curves are shown in figure 3-7. 

The following quantities are now assumed to have been determined and plotted 
for any station on the loading axis: 

S bL , the total beam load (shear) through the loading axis in pounds. 

S CL , the total chord load (shear through the loading axis in pounds. 

M tL , the torsion about the loading axis in inch-pounds. 

M bL , the beam moment in inch-pounds. 

M CL , the chord moment in inch-pounds. 

Formulas of section 3.1311 give moments and torques whose magnitudes and 
directions are not necessarily consistent with the direction of the loading axis, but the 
errors may usually be neglected. (Sec. 3.1310). 

3.133. Computation of bending stresses. The methods outlined herein are based 
on the application of the conventional bending theory to the wing section as a whole, 
rather than to individual spars deflecting independently. It is assumed that the axial 



METHODS OF STRUCTURAL ANALYSIS 



157 



deformation due to bending, for any element of the wing section, is proportional to 
the distance of the element from the neutral axis of the section. This means that in 
multispar shell wings the deflection of all spars is assumed to be substantially the same. 
These assumptions are valid only where the wing contains relatively rigid torsion cells 
so that wing twist is resisted by shear in the walls of these cells rather than differential 
bending of the beams. Experience indicates that this simple bending theory is satis- 
factory for the practical design of shell wings if allowances or corrections are made for 
the following conditions: 

(1) Excessive shear lag, or shear deflection, in the shell bet wo 311 various bending 
elements. Such deflections cause the actual stresses in elements remote from the vertical 
shear webs to be less than, and the stresses in elements adjacent to the shear webs 
greater than, the values indicated by the simple bending theory. In some types of 
structures as described in section 3.1330 (5), these deflections may be considered 
negligible in the design of the wing as a whole. Since the bending elements receive and 
give up their axial loads through shear in the webs or skin to which they are attached, 
local shear stresses and deflections will be intensified in the region of discontinuities in 
the bending or shear elements. Shear lag is therefore likely to be appreciable in such 
regions. A convenient method of allowing for shear lag is to assume a reduced effective 
area for the bending elements affected, in computing the section properties as described 
in section 3.1330. The stresses computed for such elements by the bending theory will 
then be too high, and, to be consistent, should be reduced in the same ratio as the areas 
used in the section properties. 

(2) The effects of torsion on the bending stresses at the corners of a box beam. 
This condition is usually dealt with after the bending stresses and shear distribution 
have been determined on the basis of the simple theory. See section 3. 1370 for discussion. 

3.1330. Section properties. A sufficient number of stations along the wing should 
be investigated to determine the minimum margins of safety. The information neces- 
sary to compute the section properties at each station selected for investigation may 
be conveniently obtained from a scale diagram of the wing section. Such a diagram 
(fig. 3-12) and accompanying data should show the following: 

(1) All material assumed acting in shear or bending (sec. 3.138) divided into 
suitable elementary strips and areas, with each such element designated by a suitable 
item number for use in tabular computations. 

(2) Thicknesses of skin and web elements, area and center of gravity of stiffeners 
and flanges, and the relative moduli of elasticity of all elements, normal to the section 
(sees. 2.1210, 2.52, and 3.138, or table 2-9). For example, the modulus of the beam 
flanges might be taken as a basic in tension and the moduli of other elements expressed 
as ratios thereto. 

(3) Reference axes from which the various elements are located. The amount of 
calculation will generally be less if the reference axes are made parallel to the beam 
and chord directions used in the loading curve determinations. 

(4) Effective widths of skin assumed acting in compression in conjunction with 
stiffeners or flanges. These should be consistent with the methods used in determining- 
allowable stresses, in accordance with section 3.138. 

(5) Effectiveness factors for bending elements which have elastic modulus different 
from the basic value selected for the wing, or which are affected by shear lag. The 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




METHODS OF STRUCTURAL ANALYSIS 



159 



final factor, c, includes both effects, and may be expressed as: f = f,x«», where e, is equal 
E 

to * Umcnt an( j e j s f ne s hear lag factor. 

TP 

-Ei basic 

A value of Ci = 1.0 indicates that the effectiveness of an element is not considered 
reduced by shear lag, while e 2 =0 indicates that it is completely ineffective. Shear lag 
may be general or local or a combination of both. General shear lag is greatest in a shell 
wing which has a major portion of the bending elements remote from the shear webs, 
relatively thin skin, and little or no taper in plan and front views. The general shear- 
lag effectiveness factors for such wings should be based on rational analysis or test 
data for similar wings, unless the spar web flanges can withstand stresses considerably 
higher than those computed by the simple bending theory (refs. 3-4, 3-9, and 3-13). 
In a wing having characteristics opposite to those described, general shear lag may be 
neglected if the spar flanges can withstand stresses slightly larger than those computed 




Figure 3-13. — Effectiveness of discontinuous stiffener. 



160 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



by the simple bending theory. Local shear lag due to discontinuities and cutouts may 
be estimated by determining e, from figures 3-13 and 3-14, or computed by methods 
of reference 3-13 



o 

53 

u 
o 

a 

•H 

u 
-p 
w 

o 

» 

■H 
> 

•73 




? 
•H 
■P 
O 
© 

w 

O 

(D 



/ 



v 



Cut-Out 
or 

Wing Tip 
W 



\ / 
/ 



/ 



V 



Effectiveness 



CQ 



V 



Figure 3-14. — Effectiveness of stringer's at cutout. 

In using figure 3-14, L may be taken as 2.5W for conventional constructions em- 
ploying stiff 45° plywood skin. A more rational value for L, applicable to all grain 
directions, may be computed from the following formula which takes into account the 
shear rigidity of the skin in relation to the axial load: 

1MW 

E'A 



L = 



I 

METHODS OF STRUCTURAL ANALYSIS 161 



where : 

W = width of cutout or tree end. 
(7 = effective shear modulus of skin. 
t= thickness of skin. 

= effective modulus of elasticity of composite section in tension or compression, 
as defined in section 2.761. 
.4 = total effective area of skin and stiffeners in tension or compression, as defined 
in section 2.761. 

With the foregoing information available, the wing-section properties may be 
computed in a tabular form, such as shown on table 3-5, the column headings meaning: 

(1) Effectiveness factor for item, e. 

(2) (a) Geometrical area of item, (A). 
(b) Effective area of item, (a ), =eA. 

(3) Beam distance of item from reference axis (yi). 

(5) Beam moment of area about the reference axis, (ayi). 
The location of the X axis, passing through the center of gravity and parallel to the 
horizontal reference axis, should next be determined by dividing / col. (5) by /■ col. (2b). 

(7) Beam distance of item from the X axis passing through the center of gravity (y). 
(9) Beam moment of the area about the X axis, (ay). 
(11) Second beam moment of area about the X axis, (ay 2 ). 

(13) Individual moments of inertia of items which are of sufficient magnitude to be 
included. 

The sum of the items in column 9 for all of the wing elements above or all of the 
wing elements below the X axis is equal to the static moment of the section Q x . The 
sum of items in columns 11 and 13 is equal to the moment of inertia of the wing section 
about the X axis. By a similar process, the wing-section properties about the Y axis 
can be determined by filling out the remaining columns in table 3 -5 pertaining to chord 
distances and moments. The X and Y axis are not necessarily the principal axes. 

The sum of all of the items in column 15 is equal to the product of inertia of the 
section about the center of gravity axes. Careful attention should be paid to the use of 
the proper signs in computing the products of inertia and in the subsequent stress calcula- 
tions. 

When effective widths are used for skin in compression, it is evident that the section 
properties may change for inverted loads, and in such cases the necessary computations 
should be repeated accordingly. 

3.1331. Bending stress formulas. The following formulas may be used for the 
computation of the bending stresses at any point on the wing section. These formulas 
are similar to those described in section 6:6 of reference 3-15, and permit the stresses 
to be computed without determining the principal axes of inertia or the section prop- 
erties relative thereto. 



/' = - 



M b y M c x 



(3:18) 



162 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



in 

rH 


Product of 
Inertia 




& 

10 




d 
Ul 

1 


3 


1 Individual 1 


O 

0) fH 


Chord 


H 




M 


to 
H 


Momenl 
Inerl 


Beam 


g 
M 




g 
M 


Oi 

H 


Second Moment 
about C-G. Axis 


o 








g 


Beam J 






\ 

Ul 

1 


y — -> 

o 

H 




foment 
,G. Axis 


Chord 






oh 
i 




First J 
about C, 


Beam 






H 


^ — . 
00 


Distance from 
Axis Passing 
Through C. G. 


Chord 


X 






' — 
* — ' 


Beam 








CD 


Moment about 
Ref. Axis 


Chord 


f 




«* 


in 


Beam 


c 

cd 






* — 




a 

O 


Chord 


it 






to 


Distai 

Ref, 


Beam 










as 

o 




9ATq.0©JJ3 




W II 




















sm©q.i 







g & 

M M 

i "h 

■ ■ 



METHODS OF STRUCTURAL ANALYSIS 163 



M b -M c ~f M c -M b -f 
where: M b = - ' and M, 



j (I xy) S j {I zv) 



I x % v ^ x I V 

The values of and M c are the values of the bending moments about the X and Y 
axes, respectively, used in the section properties computations; the / values are de- 
termined by the methods outlined in table 3-5, and the x and y values are the distances 
to the points at which the bending stresses are desired. 

If the analysis of some of the wing sections indicates that the value of I xV is ap- 
proaching zero, it is apparent that the reference axes chosen are nearly parallel to the 
section principal axes, and the analysis of similar wing sections may be simplified by 
omitting the computation of the product of inertia in table 3-5. The expression for the 
stress at any point in this case simplifies to: 

f , = _M*_M<y (3;19) 

* x 1 y 

When desired, the angle of inclination of the principal axes of inertia to the XY 
axes is given by the following relation (fig. 3-12): 

Tan#6=y^ff (3:20) 

where the values on the right side of the equation are obtained from table 3-5. 

The stress/' computed by the formulas applies directly only to elements having the 
elastic modulus selected as basic for the section, and a shear-lag effectiveness factor of 
1.0. The actual stress/ for other elements is obtained by multiplying/' from the formulas 
by the proper effectiveness factor from table 3-5. 

3.134. Secondary stresses in bending elements. 

(a) Air loads and bending deflections. Stiffeners are normally subjected to combined 
compression and bending. The compression results from the stiffener acting as a part of 
the flange material of the entire section. Two of the conditions producing bending in 
the stiffeners are : Part of the normal airload on the skin being carried to the ribs by the 
stiffeners, and curvature of the stiffeners due to bending deflection of the entire wing. 
Allowance for these bending loads may be made by using conservative values for the 
allowable compressive stress or, in relatively large rib spacings, by suitable computations 
and tests. 

(6) Diagonal tension-field effects. When the wing covering buckles in shear, addi- 
tional stresses may be imposed on the spanwise stiffeners by the diagonal-tension- 
field effects in the skin. If the initial buckling shear stress is greatly exceeded, it may be 
necessary to make additional analyses to account for the increased stiffener stresses. 
Shear buckles (diagonal-tension fields) in curved skin tend to produce bending or sag- 
ging of the stiffeners between the ribs. Particular attention should be paid to the possi- 
bilities of the sagging type of failure in spanwise leading-edge stiffeners, especially when 
they are also subjected to combined beam and chord compressive loads. Combined 
loading tests or conservative allowable stresses based on simple tests in accordance with 



164 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRU( 'TITRES 



section 3.1381 should therefore be employed for D-nose spar and similar types of w ings, 
(c) Bending stresses due to torsion are discussed in section 3.1370. 
3.135. Computation of shear flows and stresses. 

3.1350. General. The methods outlined herein are based on the following princi- 
ples: (refs. 3-5 and 3-11). 

(1) The shear flow.? producing bending in the wing (direct shear) are distributed 
by the various shear elements to each ending element in such a manner as to produce 
the increase in axial load per unit of span required by the bending theory. In applying 
this principle, use is made of the computations performed in determining the bending 
stresses, and the results are affected by the same basic assumptions and limitations. 

(2) The shear hows in the various shear elements of a torque box or cell are as- 
sumed to produce (or resist) torque about a reference point in accordance with the 
elementary principles of shear flows, as illustrated in figure 3 15. This assumption is 
valid only where: The ribs and bulkheads are rigid in shear in their own plane, particu- 
larly at concentrated loads; the length of the torque box, or the distance from the section 
where a large concentrated torque, applied to the section where it is reacted, is relatively 
greater than the cross-sectional dimensions of the box ; and where the cross sections of 
the wing are free to warp when the wing twists, as in a w ing panel which is so joined to 
the center section that only the main beam can transmit bending, the remaining webs 
being pin-jointed. When any of these conditions are seriously violated, conservative 
overlapping assumptions should be made as to the shear in the various elements. 

3.1351. Shear flow absorbed by bending elements. The rational methods for 
shear distribution first require the determination of the shear flows absorbed by the 
individual bending elements which may be determined by one of the following methods: 

(1) Spanvrise method. The spanwise method requires the calculation of the total 
axial load in each bending element at various stations along the span. The change in 
axial load per inch of span at any point is then equal to the shear flow being absorbed 
by the element at that point. 

This method takes account of beam taper, discontinuities and redistribution of 
bending material, and is therefore particularly applicable to complex structures where 
these conditions are involved to a considerable degree. The average axial stress, /', 
(in terms of tLd "basic" elastic modulus) in each element having small depth compared 
to the whole section at a particular station may be obtained by substituting the x and y 
coordinates of the centroid of the element in the bending stress formula of section 3. 1331. 
The total axial load, P, equals f'Xa, where a is the effective area of the element from 
the section properties computations. The shear flow, Aq, absorbed by the element is: 

A t =% (3:21, 

dP . . 
where — is obtained by plotting P against the distance, Z, along the span, and finding 
dZ 

the slope of the tangent at desired points. Aq may be most conveniently found by 
tabular methods, that is: Aq = (P J — P 1 )/ Az, where P t and P 2 are the axial loads at 
two adjacent stations and Az is the distance between them. Aq is considered positive 
when it tends to increase the tension on an element, proceeding from outboard to in- 




(b) RESULTANT SHEAR 




(o) TWIST OF SHEAR CELL 

Symbol* 

<?=shear applied per inch of shear element in section view. I Lb. per in.) 
>S'= resultant of total shear acting on shear element. 
s= length of median line of shear element in section view. 
i=thickness of shear element. 

f.= shear stress (psi.) = - 
t 

h= length of chord joining ends of shear element. 
o= reference point about which torque is taken. 

A = area enclosed between median line of shear element and radii drawn from extremities to 0. 
f)= angle of twist of shear cell (radians) per inch of length normal to the section. 
G= modulus of rigidity of portion of cell wall. 
T= torque about reference point. 

Figure 3-15. — Properties of shear flows. 





(b) 

Figure 3-16. — Sign conventions for shear flows. 

(2) Section method. The section method determines the shear flow absorbed by 
the bending elements by considering one section at a time under the external shears 
at that section, with separate corrections, if desired, for the effects of wing taper. This 
method is obviously not correct for sections in the vicinity of cutouts on wings having 
distributed bending material. It is, therefore, more applicable to wings where the 
bending material is concentrated in beams which taper uniformly. The shear flow 
absorbed by any bending element is obtained from formulas similar to those for the 



METHODS OF STRUCTURAL, ANALYSIS 



167 



bending stresses (equation 3:18), using the same section properties computations, 
as follows: 

Ag==a r_^_^] (3-22) 



T= -j-^f- (3:23) 

< v 1 xy) 

D = 



1 (IxvY C3:24) 
where : 

a = effective area of element. 

x and y are coordinates of controid of element from section diagram. Deep ele- 
ments, such as solid spars, should be broken into smaller elements. 
I x , table 3-5. 
I v , table 3-5. 

I zy =y axy, col. 15, table 3-5. 

S6'=the total external beamwise shear (parallel to the Y reference axis for the 
section) resisted by the shear elements at the section, positive upward. It may include 
a shear correction due to taper in depth, as described in section 3.1352. 

S c '=the total external chordwise shear (parallel to the X axis) resisted by the shear 
elements at the section, positive rearward. It may include a shear correction due to 
taper in plan view. 

3.1352. Shear correction for beam taper. When a beam having concentrated 
flanges is tapered in depth, a part of the external shear at any station is resisted by 
components of the axial loads in the flanges, as shown in figure 3-17. That part of the 

M 

shear resisted by the flange axial loads is: AS= — , where M is the moment at the 

L o 

station and L is the distance from the station to the point where centerlines of the 
flanges would meet if prolonged. The shear resisted by the shear elements is then: 
S'b = Sb~ A»Sb. If the flange material is distributed over the wing surface a conservative 
average taper may be assumed. These corrections for taper should not be used with 
the spanwise method of determining shear flow absorbed by bending elements. 

3.135 3. Simple D spar. The type of structure considered under this heading is 
shown in figure 3-18. The method described herein is rational in regard to beamwise 
shear and torque if the following idealizing assumptions are applicable. The beamwise 
bending material is assumed concentrated in flanges at the vertical web; the leading 
edge is assumed to be thin, that is, not capable of carrying beamwise bending, and the 
leading edge strip (or equivalent material resisting chordwise bending), is assumed to 
be located so as not to be affected by beamwise bending nor to incline the principal 



168 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



M 




&S b > portion of shear resisted by axial loads in flanges of tapered beam 

V. 

Figure 3-17. — Shear correction for tapered beam. 

axes to the vertical web. As in any single cell, the shear How is statically determinate, 
and, under the above assumptions, readily apparent. If the external loads are transferred 
to a point on the neutral axis in the vertical web, as shears parallel and perpendicular 
to the web, and a torque about the point, as shown in figure 3-18, the parallel shear, 
S'b, is resisted entirely by the vertical web, so that qb = S'b/h, where h is the height 
between the centroids of the flanges. The torque, M t , is resisted by the torsion cell, 

M t 

requiring a shear flow around the periphery: q t = — , where A is the enclosed area. 

2A 




< d 



Figure 3-18. — Shear in simple D-spar. 

The shear S' c is assumed resisted equally by the upper and lower skin, so that: 
q c = S' c /2d, where d is the distance from the vertical web to the leading edge strip. 

Then: q w (vertical web) =q b — q t ; and qL.E.=qt + q e , with the sign conventions 
shown on the diagram. 



METHODS OF STRUCTURAL ANALYSIS 



169 



If the bending material of a D-spar is largely distributed around the periphery in 
the form of a thick skin or spanwise stiffeners, the general rational method for single 
cells, described in the following, is more applicable. 

3.1354. Rational shear distribution. 

3.13 540. Single cell — general method. The following method is applicable to 
single cell structures having the bending material distributed in the form of a thick 
skin or any number of concentrated flanges or stiffeners. However, when such material 
is in the form of thick skin, it is assumed divided into strips each of which is considered 
a concentrated element. Since the single cell is statically determinate, the elastic 
properties of the shear material are not necessarily involved in determining the stress 
distribution, although they are required in determining the twist or shear center. For 
simplicity, the shear center will not be used in computing shear flows and stresses. Its 
location may be readily determined after the shear flows are known. The method of 
computing shear flows is briefly outlined as follows: Referring to figure 3-19, the shear 
flow in the main vertical web is considered as an unknown, q,„, and the shear in each 
successive shear element around the periphery of the cell is expressed in terms of q m by 
successively adding (algebraically) the shear flows, Aq,„ absorbed by the bending 
elements. The sum of the torques due to each shear element, about reference point 
in the main vertical web, is then computed from the principles of shear flows (figure 3-15) 
and equated to the external torque, M t . This equation is solved for q m , and the numerical 
values of the remaining shear flows obtained by successive addition of the Aq values, 
as explained. By using a suitable notation, the computations may be reduced to a 
simple tabular form as shown on table 3-6. 

Such a notation is described as follows, and is illustrated in figure 3-19, where 
the assumed positive directions of quantities are as shown: 

M t = the resultant external moment applied at point when the external shear 
Sb and SJ have been transferred to that point. 
q m = shear flow in main web. 

2ij <?2, q%, etc., are shear flows in successive shear elements numbered clockwise 
around the section, as shown. 

q n = shear flow in nth shear element. 

Aq,, Aq 2 , Aq Jt etc., are shear flows absorbed by bending elements correspondingly 
numbered. Aq is positive when it tends to produce tension in the bending element, as 
shown in figure 3-16. It is produced by (or requires) a resultant shear flow directed 
away from the element in section view. The values of Aq are assumed to have been 
determined by methods such as those of section 3.1351. 

A(?„ = shear flow absorbed by nth shear element. 

A lt A e , A 3 , etc., are the areas enclosed between shear elements and radii from the 
reference point, 0, to centroids of the bending elements. 
A = enclosed area of entire section. 
T = total torque of shear elements about point 0. 

n 

y =summation of quantities for elements 1 through n, where n — 1, 2, 3, etc. 

T~ 

N = number of last bending element (lower main flange). 
N—1 =number of last shear element (not counting main web). 



170 



AJSTC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 
Table 3-6. — Shear-flow computations for single cell. 



(1) 


(2) 


(3) 


U) 


(5) 


(6) 


n 




t Aq n 

• n 

= £(2) 
l 


An 


VlAq n 
= (4>x(3) 




1 

2 
3 

N-1 


A % 




A 

A 3 

r 






N 




X 


X 








N 

2>) 
1 




N-1 

i 


N-1 

21 (5) 
1 




N 

/ (2) should approximate 0, 
Note: Z— 
1 
N-1 

^ (4) should approximate total area = A* 
1 



METHODS OF STRUCTURAL ANALYSIS 



171 



The expressions for shear now in any element in terms of q m , using sign conventions 
of figure 3-16, are: 

Aq,=q,-q m >- Aq,=q m + Aq, 

Aq i = q sl — qi >- Aq,=q m + Aq, + Aq s 

n 

qn = q m + } Ag„ (3:25) 

i 

Equation (3:25) is represented graphically on diagram (b) figure 3-19 by a flow q m 

n 



around the entire section, to which is added flow / Aq n at any shear element to 
obtain the total flow q n acting in that element. / 

The expression for the total torque of the shear elements about point 0, figure 3- 
19(a), is: 



or 



T = )> 2 A n q n 

T \~ 

ir—/ A,,q n , which, from diagram (b) 

Li '- 



of figure 3-19 




(A n > A<?„) 

1 
Mi 

=- — (equilibrium of internal and external loads) 



Aq m =-^-) (A n > Aq n ) 

Z —j— 1 



vm- 2A A y (i.) A ?B ) (3:26) 

Equations (3:25) and (3:26) may be represented in the tabular form shown by 
table 3-6. Equations (3:25) and (3:26) and table 3-6 are directly applicable to stiff ened- 
Z)-nose type wings if the sign conventions and numbering shown in figure 3-20 are 
employed. 

3.13541. Two cell — general method. The following method is an extension of the 
general method for single cells. The two-cell structure is statically indeterminate since 
the division of the total torque between the two cells depends upon their relative torsional 
stiffnesses. A shear flow in an element of the front cell and a flow in an element of the 
rear cell are therefore considered as unknowns, and the flows in the remaining elements 
expressed in terms of these two unknowns. One independent equation is obtained from 

/ torques = 0, and another from the fact that the twist of the front cell equals the 

twist of the rear cell. The two unknown shear flows are obtained by simultaneous 



172 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 





(b) GRAPHIC REPRESENT A? IOH OF SHEAR FLOW E<JOATKKS 

Figube 3-19. — Rational shear flow — single cell. 



METHODS OF STRUCTUKAL ANALYSIS 



173 




Fioure 3-20. — Conventions for stiffened-D nose section. 



solution of these equations, and the remaining flows computed by successively adding 
or subtracting the shear flows absorbed by the bending elements. The notation is il- 
lustrated in figure 3-21, where the following symbols are additional to those described 
in section 3.13540 for single cells. 
q m = shear flow in main web. 

q f = shear flow in first shear element (numbered 0) of front web. 

s , s,, s s , . . . s„, are lengths of shear elements. 

Co, c,, o, . . . c„, are elastic constants of the shear elements. 

c=— , where t e is the effective thickness of the shear element, that is: t e = t, X— , 
tl G 
where t t is the geometrical thickness of the element, G,, the shear modulus of the 
element, and G the shear modulus of the material considered basic for the section (section 
2.52). If a particular element is expected to buckle appreciably in shear, the value of 
Gj should be reduced accordingly. 

A F = enclosed area of front cell. 

A r = enclosed area of rear cell. 

A =A F +A B . 




n 

y = summation of quantities for elements 1 through », where n = l, 2, 3, etc. 

1 

N = number of upper flange of main web. 

M = number of lower flange of main web. 

Subscripts f and r refer to front and rear cells, respectively. 

Shear flow in any shmr element (see derivation for single cell). 

Front cell: ^ — 

q. nF = q f +l A 9 „ (3:27) 

1 



METHODS OF STRUCTURAL ANALYSIS 



175 



Torque about point 0. 

T v 



y A„q n , which from diagram (b), figure 3-21, 



N-l 



= q-A+ qm A R +y (A n > A 9 „) 

1 

=--- (External torque) 



q f A+q m A K = ~-) (A„ ; \q n ) 



A R M, 1 



1 1 
N-l n 



^-f^~^l_ (A„>__A,J (3:29) 

which may be written in the form 

X g q f +.Y B q m = Z 2 (3:30) 

Where X 2 , Y and Z 2 are numerical constants, and q } and q m are unknown quantities. 

Consistent deformations. The angle of twist 6 is the same for front and rear cells. 
Therefore, 

'=^^—4: (3:31) 

for each cell, where the summation is taken entirely around the cell. (fig. 3-15). 

1 



2G% = -. — > qc (3:32) 

G is taken out of the summation sign as a constant, since all elements are reduced 
to a common basic shear modulus by«use of effective thicknesses. Therefore: 



A p A p 



qc=-j- qc 



R 



q c = R ) qc, which is from diagram (b) of figure 3-21: 

M — 1 M-l n N- 1 N-l n 



q f y c n +y (c n y h.q n ) — q m c m =Rq, c n +R ) (c n ) Aq n ) 



1 M M 1 

N — 1 

+ Kq m y c„ + Rq,„c m (3:33) 

M 



176 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



or 

M-l N-l N-l N-l n 



9/0 c n — Fty c„) — q m (e m +~Rc m +Ry__ c„)=R~y (c n ) Aq n ) 

IT M ~M~ ~~M~~ T~~ 



M-l 



n 



(c„> Aq„) (3:34) 

1 1 

which may be written in the form 

X lfJr +Y,q m = Z, (3:35) 

The quantities q f and q m are then determined by solving equation (3:30) and 3:35) 
simultaneously. The summation terms in these equations may be computed in a form 
similar to table 3-7. 

3.13542. Two-cell, four-flange wing. If it is assumed for this type of wing (fig. 
3-22) that the skin and web members carry shear only, the general equations given in 
section 3. 13541 can be written in the following form : 

. M 3__ n 

Qr+-f 9 m =jj—j > " (A n y A<?„) (3:36) 

8 .3 3 n 



q,{Co-R) f„)-q m (c m + Rc m + R,y C B )=#> (c„> - Aq n ) (3:37) 



/ / 1 



These equations may be expressed as follows : 



X £ q f +Y g q m = Z s (3:38) 
X 1 q f +Y,q m = Z 1 

(3:39) 



where: 



X, = l (3:40) 
Y, = ^f (3:41) 



M t 1 ' 



z?= M~i> {An >- _ A «-> (3:42) 



X,=c a -Ry c n f3:43) 



V, ^-(c m + Rc m +Ry c„) (3:44) 



178 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



*' =R > (c»> Aq n ) (3:45) 

1 i 

Then, solving (3:38) and (3:39) simultaneously, 

I±Jt± (3:46) 

SHEAR FLOWS SHOWN IN ASSUMED POSITIVE DIRECTION 




S b ' = + 100,000 pounds. 

&' = - 10,000 pounds. 

M t = - 500,000 inch-pounds. 

Aq values, as listed in table 3-7 (determined by sec. 3.1351 (2) ) 
S, t e , and A values as listed in table 3-7. 
-4^ = 2,288 square inches. 
= 2,912 square inches. 
A =5,200 square inches. 
Shear flow values, obtained by substitution of the summations from table 3-7 in 
equations (3:40) to (3:47) are as follows: 
q f = 154.3 pounds per inch. 
q m =2,140.4 pounds per inch. 

The remaining shear flow values are then determined from equations (3-27) and 

(3:28): 



METHODS OF STRUCTURAL ANALYSIS 



179 



q, = — 89 pounds per inch. 
q,— —548.1 pounds per inch. 
g,, = 36.8 pounds per inch. 

3.13543. Shear centers. For some purposes, it is desirable to determine the shear 
center of a wing section. As derived herein, the shear center is defined as the point on a 
wing section at which the application of a shear load will produce no twist in a differential 
length of the structure beyond the section. A point so determined is a true shear center 
for the wing as a whole only if the wing is of constant section throughout the span, or 
tapers in a manner so that all sections are geometrically similar. 

In the following formulas, symbols not expressly defined are the same as in sections 
3.13540 and 3.13541. 

(a) Single cell. Assume that a V load of value P has been applied to the section and 
the values of frqiov the bending elements computed according to section 3. 1351 : 



Twist = 6 = = 



SAG 



/ 



qc 



(3:48) 



qc is found by inspection of figure 3-19 and equation (3 :25), resulting in : 

N — l N-l 



n 



C n + 



/ 



\ 



(3:49) 



1 1 J 

Equation (3 :49) is solved for the value of q m which will produce no twist : 

N-l n 



(Cn 



1 



1 



N-l- 



(3 :50) 



c m + 



Cn 



1 



Let x = the horizontal distance from the origin to the load P for the condition of 
no twist. (That is, x = distance to shear center). Since Px = M t , x may be determined 
from equation (3:26), as follows: 

N-l n_ 

(3:51) 



Pr 1 



q "' 2 A A 



(A n y \q n ) 



1 



2A 
P 



N-l 



q m + 



A 



{An 



a 9 „: 



(3:52) 



where q m is from equation (3:50) and other terms are computed as in table 3-6. 

The vertical location of the shear center may be determined, if desired, by applying 
a drag load and proceeding as has been shown. 

(b) Two-cell. It is assumed that a V load of value P has been applied at the shear 



180 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



center which is at an unknown horizontal distance x from the origin 0, and that ^q 
values corresponding to load P have been computed for the bending elements. Since the 
twist of both cells is zero: 



1 



0/, = O = -j-> qc (3:53) 



R 



6« = 0=^-> qc (3:54) 



Substituting for y qc, according to section 3.13541: 
M—l M-l n 



'y=0 = g/> c n -q m c m +y (c„> Aq n ) (3:55) 

11 

N-l N-l N-l 



n 



6«=0 = 9 / > t- „+(/„, ( _c n +c m )+) (c n ) Aq n ) (3:56) 

M M M 1 

Solving equations (3:55) and 3:56) simultaneously for (//and q,„ will give the values neces- 
sary for the condition of no twist. Since Px is the torsional moment about the origin 0, 
this moment and the value of x may be found from the derivation of equation (3:29), 
as follows: 

M P M-l n 

-l=-^ = q f A + q n A R +y (A n y Aq n (3:57) 

1 1 

where the values of gyand q m arc from equations (3:55) and 3:56). The vertical location 
of the shear center may be determined, if desired, by applying a drag load and proceeding 
as in the foregoing. 

3.136. Ribs and bulkheads. 

3.1360. Normal ribs. Normal ribs (those subjected primarily to airloads), in a 
shell wing, receive the airloads from adjacent skin and stiffeners and redistribute them 
to the various shear elements of the wing section. The strength of such ribs is always 
proven by strength tests, but a picture of the stress distribution is useful in rib design 
and m devising suitable test set-ups. The required airloads, distributed in accordance 
with the airfoil chordwise pressure distribution, may be considered as the applied loads 
on the rib, and the shear flows applied by the rib to the various wing section shear ele- 
ments, oppositely directed, as the reactions. Such shear flows may be determined by 
performing computations similar to those for the shear flow distribution (using the 
section method, sec. 3.1351 (2) ), after resolving the airloads into resultant forces and 
a moment, at a convenient reference point. 

These conditions may be simulated in a test by constructing a short spnawise 
section of the wing in which the test rib at one end forms the loading bulkhead, while a 
bulkhead at the opposite end supports the whole section. The spanwise length, and the 



METHODS OF STK U( TUKAL ANALYSIS 



181 



attachment of stiffeners and skin to the support bulkhead, should be such that the rib 
loads are not transmitted directly to the support bulkhead by these elements acting as 
cantilever beams. 

Normal ribs are also subject to a variety of secondary loads, for example: Loads 
resulting from their function as compression elements when the skin buckles into diagon- 
al-tension fields due to shear; and loads resulting from the axial forces in stiffeners and 
skin while the wing is deflected in bending. 

3.13600. Rib-Crushing Loads. Compressive forces in the upper surface material 
of the wing, while it is curved upward by bending deflections, produce downward acting 
loads in the ribs, while the tensile forces in the lower surface produce upward loads, 
thus subjecting the ribs to compression or crushing in the vertical direction. Where an 
appreciable portion of the wing-bending material is distributed in the form of skin and 
stiffeners remote from the beam webs, the rib-crushing loads should be investigated by 
methods such as reference 3-10 or the following : 

PL PLM 

w= -r=-eT (3:58) 

where : 

if = vertical crushing load on rib flange, in pounds per inch of chord. 

P = spanwise axial load: in wing surface material due to bending, in pounds per 

inch of chord, at given point on wing section. 
L = rib spacing, inch. 

R = radius of curvature of wing due to bending. 

M = bending moment on wing section. (Mb from section 3.1331 may be used as 
an approximation.) 

/= moment of inertia of wing section. (I x from table 3-5 may be used as an 
approximation.) 

E = basic modulus of elasticity used in computing section properties. (Sec. 3.1330. ) 

3.1361. Bulkhead ribs. Bulkhead ribs are described as those that distribute 
loads of appreciable magnitude, other than air loads, to the wing-section shear elements; 
for example, fuselage, landing gear, and fuel tank reactions. Such loads, as well as the 
airloads, may be considered as external loads applied to the rib, and the shear flows 
applied by the rib to the shear elements, oppositely directed, as the reactions. Here, 
however, one or more of the conditions required by the shear-flow theory (sec. 3.135) 
will generally be violated. For example, a larger amount of shear may be absorbed by 
the elements nearest a concentrated load, depending on their rigidity relative to that of 
the bulkhead. Conservative overlapping assumptions should therefore be made. 

Bulkhead ribs may also perform the function of redistributing shear among the 
shear elements of a wing wherever some of these elements are discontinued or bending 
elements redistributed. The shear flows from the outboard wing section may then be 
considered as the applied loads on the rib, and the shear flows applied to the inboard 
section, oppositely directed, as the reactions. 

Likewise, at a rib where any wing element carrying an appreciable axial load 
changes direction, the axial loads in the inboard and outboard portions of such an ele- 
ment should be resolved into components parallel and perpendicular to the plane of 



182 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



the rib. The resultant of the components in the plane of the rib may then be considered 
as a load applied to the rib, with reactions supplied by the wing-section shear elements 
as described previously. 

As a result of the bulkhead analysis, it may be necessary to revise the shear distri- 
bution determined in the general shear analysis (sec. 3.135) for local conditions. 

3.137. Miscellaneous structural problems. 

3.1370. Additional bending and shear stresses due to torsion. The corner flanges 
of a box beam are theoretically free from axial (bending) stresses under a pure torque 
loading, if the cross sections are free to "warp" as the box twists. However, in a shell 
wing where more than one beam is continuous through the fuselage, either directly or 
through an equivalent structure, bending stresses will be induced in the corner flanges 
since the opposing action of the opposite wing will restrain the root sections from warp- 
ing. Additional shear in the short sides of the box is also induced at restrained sections. 

In wings not subjected to unusual torque loads and in which the torque cells are 
continuous and enclose a large part of the sectional area of a reasonably thick wing, 
the bending stresses at the root due to torsion should be small compared to the total 
bending stresses for the loading conditions producing maximum bending in the wing. 

Analytical methods for computing the bending stress due to torsion in various 
types of box wings are described in references 3-8 and 3-12. Where the shear rigidity 
of one wall of a box wing is greatly reduced by a cut-out, the wing torsion should be 
assumed to be carried as differential bending in the spars in the region of the cut-out. 
Rational solution of the general case is given in reference 3-6. 

Wings in which the torsional stiffness of the torque cells is relatively small because 
of the small enclosed area or because of many large cut-outs may be conservatively 
designed as independent spar wings. The effect of the torque cell in relieving the critically 
loaded spar by transferring part of the load to the other spars may, however, be esti- 
mated according to reference 3-7. 

3.1371. General instability. Reference to section 3.1381 shows that the column 
length of spanwise stiffeners is generally taken equal to the rib spacing. Such an as- 
sumption is valid only when the ribs act as rigid lateral restraints for the stiffeners at 
the points of intersection. If the ribs lack rigidity in their own planes, allowing the 
stiffeners to deflect laterally, the axial compressive loads in the stiffeners tend to further 
increase such deflections because of the resulting eccentricities. If the rib rigidity is 
too low relative to the axial stiffener (or skin) compressive loads, a state of equilibrium 
will not be reached, and the ribs and stiffeners will collapse simultaneously. In con- 
ventional wings with full depth ribs, the condition described above, known as general 
instability usually need not be considered. If shallow ribs (at tank bays and wheel 
wells) or truss-type ribs having shallow flanges are used in wings where a large part of 
the bending compressive loads are carried in surface material remote from the wing 
beams, analysis or tests for this condition should be made (ref. 3-14). 

3.138. Strength determination. The analytical determination of the strength of 
the structure is based on a comparison between the computed internal stresses, and the 
allowable stresses obtained by static test or calculated from the material properties by 
methods such as those of chapter 2. In order that the computed margins of safety so 
obtained may represent the strength of the structure with respect to the specified ex- 
ternal loads, as accurately as possible, all conditions and assumptions on which both 



METHODS OF STRUCTURAL ANALYSIS 



183 



the internal and allowable stresses are based should be reviewed, and any necessary 
adjustments or allowances made, prior to the final comparison showing the margins of 
safety. Such allowances may be made by arbitrarily increasing the originally computed 
internal stresses or decreasing the allowable stresses, in the light of the review. 

Some of the factors to be considered in the strength determination are discussed 
under the following subsections. 

3.1380. Buckling in skin. For a structure in which the major portion of the 
compressive loads due to bending are intended to be resisted by the skin, with the 
shape being maintained by comparatively light reinforcing structure, the critical 
buckling and ultimate stresses for the skin, whichever is lower, should be considered 
as the allowable stress. When buckling does not occur, the ultimate allowable stresses 
may be computed by the methods of sections 2.60 and 2.61. The criteria of sections 
2.70, 2.80, and 2.82 may be used as guides in predicting the occurrence or nonoccurrence 
of buckling, but the strength of such structures should be substantiated by static tests 
of the complete structure, or of a closely similar structure, to ultimate load, because 
of the uncertainties of buckling phenomena. 

For structures in which the supporting and stiffening members are capable of 
withstanding a major portion of the compressive loads, buckling of the skin does not 
necessarily result in failure, as discussed in the following subsections on stiffened panels 
and shear elements. Sharply curved skin panels have much higher critical buckling 
stresses than flat panels of the same dimensions, but failure in curved panels usually 
occurs immediately after buckling begins. 

3.1381. Compression elements. Where secondary stresses, such as those de- 
scribed in sections 3.1330 (5), 3.134, and 3.1370 have not already been taken into ac- 
count, a reasonable increase in internal stresses should be assumed for critical elements 
affected thereby. Although wood will yield slightly in compression, tending to relieve 
the highly stressed fibers, elements which have undergone some crushing in compres- 
sion may fail at unexpectedly low tensile stresses when the load is reversed. 

When light span wise stiffeners are used to reduce the size of the skin panels rather 
than to resist the wing bending loads, they need not be designed to withstand the stresses 
which would be assigned to them as isolated structural elements by the bending theory, 
provided that such stiffeners are designed to accommodate themselves to the spanwise 
shortening of the compression side of the wing without failing. At locations remote 
from the spars, this can be accomplished by making the stiffeners sufficiently flexible 
so that they can bow between the ribs without failing. Such stiffeners may tend to 
separate from the skin, however, unless special precautions are taken. At locations 
adjacent to highly stressed spar flanges this accommodation may be obtained by using 
a cross section and material such that local crippling and crushing failure will not occur. 

3.1382. Stiffened panels. In structures where the skin is expected to buckle 
below ultimate load and the reinforcing structure is designed accordingly, the allow- 
able compressive stresses may be obtained from section 2.76 or from tests on stiffened 
panels. 

(a) Effective widths. In both the allowable and the internal stress computations, 
an effective width strip of skin adjacent to each stringer is assumed fully effective in 
compression. The width is often selected arbitrarily, and it is sometimes assumed 
that the value selected makes little difference so long as the value used in the section- 



184 



AN (J BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



properties computations is consistent with that used in computing allowable stresses 
from the total load supported by a test panel This assumption would be true if the 
upper and lower bending material of the wing consisted only of two symmetrical panels 
(with the same effective widths in tension as compression) but it may lead to some error 
if the bending material is not structurally symmetrical and the usual methods of com- 
puting section properties are used. Therefore, for structures in which the skin carries 
a considerable portion of the bending load, the effective widths should be determined 
as accurately as possible, either by theoretical methods, such as those of section 2.760, 
or by accurate strain-gage measurements on the test panels. The effective width, 2w, 
of plywood panels, is usually expressed as a strip that is considered to act at a stress 
corresponding to that of the unbuckled plywood at the same deformation as the stiffener. 
(Sec. 2.760.) The effective width of metal panels is usually expressed as a strip acting 
at the same stress as the stiffener. The basis for the effective widths indicated in a 
particular analysis should, therefore, be clearly stated. 

(b) Allowable compressive stresses. In determining the allowable compressive 
stress, the various possible modes of failure discussed in section 2.7610 should be con- 
sidered. When the allowable stress is computed by section 2.761, the stiffener plus 
effective width of skin is considered as one composite element having an effective mod- 
ulus of elasticity E'. This procedure was arranged to facilitate checking the stress in 
any ply or fiber of either plywood or stiffener. Such a composite element may be con- 
sidered as one item in the section-properties computations (sec. 3.1330), where e t will 

E' 

equal — basic. The computed internal stress, /, for comparison with the allowable 
E 

will then be : / =/' X e, where /' is the fictitious basic-modulus stress obtained by the 
bending formulas in section 3.1331, and e is the total element effectiveness factor in 
accordance with section 3.1330 (5). 

When the ribs are sufficiently rigid in their own planes (sec. 3.1371) the column 
length of the stiffened panels is taken as equal to the rib spacing. In regard to the 
column-fixity coefficient to be used in conjunction with this column length, it is noted 
that typical structures show a general tendency to bow inward in the bays between 
ribs, but a few bays will tend to bow outward. Where one bay bows in and the next 
out, a fixity of approximately c = 1.0 is developed, depending on the rotational fixity 
furnished by the ribs and the degree of buckling and plate or curvature effect of the 
skin. A value of c = 1.5 may be assumed if the stringers are fixed to ribs having appre- 
ciable bending stiffness in a vertical plane parallel to the stringers. Higher values 
should not be used in design unless substantiated by tests on a complete structure. 

In flat-ended-panel tests, a value of c = 3.0 or more is usually developed. The 
results of such tests must therefore be corrected to the fixity value used in the design 
of the structure. 

(c) Combined stresses. A convenient method of considering the effects of combined 
compression and shear in stiffened panels is the stress ratio or interaction curve method, 
that is, R m +R a n = 1.0, where R c is based on the allowable compressive stress discussed 
in paragraph (b), and R s is based on the strength of the panel in pure shear. 

The exponents m and n may be assumed equal to 2.0 for panels which are sub- 
stantially flat, but not more than 1.0 for sharply curved panels, such as in D-nose spars, 
unless tests are made under combined loads to determine points on the interaction 



METHODS OF STRUCTURAL ANALYSIS 



185 



curve. For D-nose spars, tests to ultimate load should be made. A portion of the 
spar of sufficient length to eliminate end effects, may be used in such tests. 

3.1383. Tension elements. Tension elements of wood yield very little, compared 
to metals, before reaching their ultimate strength. Unaccounted-for secondary stresses 
or unconservative assumptions in the stress analysis are therefore likely to cause fail- 
ures. Since the plywood skin, stiffeners, and spar flanges on the tension side of a wing 
may not reach their ultimate strengths at the same time, the stresses in each element 
should be determined and compared with the corresponding allowables. For plywood 
having the face grain parallel or perpendicular to the spanwise direction, the modulus 
of elasticity for use in determining section properties and internal stresses may be 
obtained from section 2.52, or table 2-9, and the allowable tensile stress from section 
2.601, and table 2-9. For plywood having the face grain at an angle to the spanwise 
direction, the spanwise modulus of elasticity may be obtained from section 2.56. For 
the special case of plywood with face grain at 45° to the span, the value of E may be 
obtained as described in section 2.56110. The allowable tensile stress for such 45° 
plywood may be obtained from section 2.611 and table 2-9. 

When the plywood on the tension side does not buckle due to shear, which is usually 
the case on a wing (sec. 2.702), the condition for failure under combined tension and 
shear may be determined by stress ratios in accordance with section 2.613. 

3.1384. Shear elements. When the shear flow, q, has been determined, the internal 
shear stress is obtained by dividing q by the actual thickness of the element, even though 
an effective thickness based on relative moduli of rigidity was used in the shear dis- 
tribution analysis. The allowable shear stress values given by section 2.72 are directly 
applicable to beam webs and allow for the effects of the beam bending stresses near the 
flanges. 

These allowable shear stresses should also be applicable to substantially flat wing- 
skin panels in the same range with respect to buckling. The ultimate strength of 
curved panels in shear must at present be obtained from tests on specific structures as 
described in section 3.1382 (c), since buckling usually precipitates failure. 

3.2 FIXED TAIL SURFACES. The procedures applicable for use in the stress 
analysis of fixed tail surfaces (fin and stabilizer) are analogous to those described in 
section 3.1 for the analysis of wings. The nature of the applied loads is necessarily similar 
in that the source is principally aerodynamic and the spanwise and chordwise distribu- 
tions of the same are similar to those over wing surfaces. The loads resulting from 
inertia effects require a consideration similar to that employed in the analysis of wings. 
The dependence of the applicable type of analysis upon the structural arrangement 
of the material is also similar to that encountered with wings and this consideration is 
treated in section 3.1. The strength of the structure is determined by comparison of the 
calculated internal loads and stresses with the allowables which are obtained either from 
tests or from the information given in chapter 2. The determination of the strength of 
shell structures, including reinforced shells, is presented in detail in section 2.138. 

3.3. MOVABLE CONTROL SURFACES. The movable control surfaces are ordi- 
narily comprised of the ailerons, elevator, and rudder. The analysis of each of these 
surfaces is fundamentally the same basic problem. Each movable surface consists of 
an airfoil free to rotate about a hinge axis fixed on the supporting structure except as 
restrained by the control system at its attachment point (control horn). The essential 



186 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



structure is made up of the : 

(1) Airfoil surface (fabric or plywood plating) upon which the air forces act and are 
transmitted through 

(2) Surface attachment means (lacing, nails, or glue) to the 

(3) Ribs. The ribs transfer the air loads through shear and bending to the 

(4) Main beam and 

(5) Torque tubes. The beam and torque tube are supported by the fixed surface 
structure at the 

(6) Hinges where the transverse shear is transmitted to the fixed surface. The torque 
tube carries the torque resulting from the air loads and hinge support reactions to the 

(7) Horn, where it is balanced by the control system reactions. 

A satisfactory analysis should include a check of the plating material (fabric, ply- 
wood) under the imposed design pressure loading. Unit pressure loadings, consistent 
in magnitude with those encountered over deflected control surfaces should be considered 
in such a check. The strength of the surface attachments should be checked in combina- 
tion with that of the surface material itself. The most satisfactory method of determining 
the strength of such structural items is by "blow-off tests" of panels representing the type 
of construction employed (simulating rib spacing, surface attachments) when subjected 
to test pressures representing the design loadings. Critical surface pressures are usually 
negative (tending to blow the surface outward). 

Ribs may be considered as cantilever beams supported at the main beam or torque 
tube and supporting the pressure loading over the area extending approximately midway 
to adjacent ribs. Here again static tests of representative" structures constitute the pre- 
ferred basis for proof of satisfactory strength. 

The main beam and torque tube should be checked under the shear, bending, and 
torsional loads resulting from the rib loadings, and the reactions at the hinge supports 
and the control horn. When the main beam or torque tube is continuous over three or 
more hinge supports, the deflection of the fixed surface or wing under flight loads should 
be taken into account by introducing suitable deflections of the supports into the three 
moment equations or by conservative overlapping assumptions. Irregularities and dis- 
continuities of such structures are often encountered because of the cut-outs necessary 
for the control surface hinges. Care should be exercised to provide adequate strength 
and rigidity in way of such cut-outs by means of proper reinforcing and by use of con- 
servative assumptions both as to stresses developed and stresses allowed. This is es- 
pecially necessary in wood structures because of the inherent inability of wood to equalize 
stress concentrations through considerable plastic deformation. 

3.4 FUSELAGES. 

3.40. General. Most of the commonly-used types of wood fuselage construction 
fall within one of the following: 

( 1 ) Four-longeron type. 

(2) Reinforced shell (semimonocoque) type. 

(3) . Pure shell (monocoque) type. 

Examples of these types are included in the sketches shown herein under the pertinent 
subheadings. A particular airplane fuselage need not necessarily be confined to one 
type of construction but may employ any applicable combination. For example, the 



METHODS OF STRUCTURAL ANALYSIS 



187 



stiffened-shell type may revert to the four-longeron type in way of large cut-outs such as 
cockpit openings, or bomb bays. 

3.41. Four-Longeron Type. The treatment of the four-longeron type is somewhat 
analogous to that of the D-section and single-cell shells as described in section 3.13 with 
the additional simplification that results from the inherent symmetry of the typical 
fuselage section. In both, the material effective in bending is concentrated into a small 
number of locations and the section properties for use in a bending analysis may be 
calculated in the normal manner as based upon such an assumption. The plywood shell 
material will actually contribute in some indeterminate extent to the bending strength 
of such four-longeron-type sections as are illustrated in figures 3-23 and 3-24. However, 
it is probable that, on the compression side, this contribution will be limited to approxi- 
mately that corresponding to the buckling load for the plywood panels as determined 
from the transverse frame spacing, panel thickness, species, arrangement of plies, and 
curvature according to the methods described in chapter 2. In this type of construction, 
the unit deformation corresponding to the maximum design stress in the longerons very 
probably exceeds by far that corresponding to the buckling stress of the adjacent plywood 
material and of that farther removed from the neutral axis. Also, without curvature 
and without longitudinal stringers between longerons and the smaller plywood panel 
expanses and greater buckling stresses resulting therefrom, the design shearing stress 
in the sides of the four-longeron-type section will also probably exceed the buckling 
values by a considerable amount. 

Both of these tendencies lead to the conclusion that it is satisfactorily conservative 
to neglect the contribution of the plywood shell to the bending properties in cases where 
the buckling stresses of such shell material is considerably exceeded by the longeron 
stresses and shear web stresses calculated on the basis of zero contribution (fig. 3-23). 
In any event, the optimum contribution of the shell material that could be expected 
would be that corresponding, on the compression side, to the buckling stress of the panels 
and, on the tension side, full effectiveness. In this connection, the designer's attention 
is directed to the existing knowledge of the behavior of thin panels subsequent to buck- 
ling. With flat panels and panels of slight curvature (that is, those in which the con- 
tribution of curvature to the buckling load is not significant) a load approximately equal 
to the buckling load is maintained after buckling. With thick plates of considerable 
curvature (that is, those in which the contribution of curvature to the buckling load is 
appreciable) the load tends to drop off after buckling. In such panels, rupture is also 
much more likely to result at buckling. For these reasons, it is desirable that under the 
ultimate design loads, the stresses resulting in such a portion of a compression flange 
do not exceed the critical buckling stresses. On the tension side, the contribution of the 
plating should be taken as that corresponding to an equivalent area of the plywood 
flange in terms of the longeron material (fig. 3-24). For purposes of calculation, the 
equivalent effective area (or thickness) of the tension plywood flange would be equal to 

t X— where t = plywood thickness, E, = modulus of elasticity of longeron material in a 

E, 

direction normal to the section, and modulus of elasticity of plywood material in a 
direction normal to the section. These definitions are different from those used in 
chapter 2. 



188 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



A. ILLUSTRA TIN 6 SHEA/? INTENSITIES 
DUE TO VERTICAL LOAD 




REJLH 



SHEAR INTENSITY 
due to V load 

r - V 



B. ILLUSTRATING SHEAR INTENSITIES 
DUE TO SIDE LOAD 



-A^LOtidtkOH Af£A) 




[L0N6ERON 
AfiEA) 



n = SLA,b,+A?h > '] . 
5 ZI ft 

z - SA z b t 4 

h 21 h 



SHEAR INTENSITY DUE TO T DROVE Q, = J— 

fr 2A 

RESULTANT SHEAR INTENSITY a, = a + a + a 

Hv 5s OT 

BENCH NG STRESS f k = ~ - 



NOMENCLATURE 



S= SIDE LOAD (TRANSVERSE SHEAP) AT SECTION 
V = VERTICAL LOAD (VERTICAL SHEAR) AT SECTION 

r= TORQUE ABOUT INTERSECTION OF REF. AXIS WITH PLANE OF SYMMETRY OF SECTION 
% = SHEAR INTENSITY ( LBS. PER INCH RUN) 

M= BENDING MOMENT ABOUT N. A. AT SECTION (+ M CAUSES COMPRESSION IN 

UPPER AND R.H. FLANGE! MATERIAL - LOOKING FORWARD) 
1= MOMENT OF INERT/A ABOUT N.A. OF EFFECTIVE BENDING AREA 
A= AREA ENCLOSED BY SHELL 

x= DISTANCE OF BENDING MATERIAL FROM Y-Y N-A. 
y = DISTANCE OF BENDING MATERIAL FROM /-X N-A. 



Figure 3-23. — Four-longeron fuselage — plating ineffective in bending. 



METHODS OK STRUCTURAL ANALYSIS 



189 



COMPRESSION j/. 
SIDE 



TENSION 
SIDE 




*£ct.xiL if BUCKLED AT DESIGN LOAD 
t A IF UNBUCKLED AT DESIGN LOAD 



IHEFFtCllve 



A. PARTIALLY BUCKLED SHELL 




Y 

B. UNBUCKLED SHELL 



Fcr = PANEL BUCKLING STRESS 
F = LONGERON ALLOWABLE STRESS 

E z - MODULUS Of ELASTICITY OF PLYWOOD NORMAL TO SECTION 

E, = Modulus of elasticity of longeron normal to section 

Figure 3-24. — Four-longeron fuselage — plating effective in bending. 



190 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



In determining the optimum effectiveness of the compression plywood material, 
it is emphasized that the total load carried by the material would be approximately 
limited to the buckling load rather than being proportional to the total load upon the 
section. If it is considered permissible for the subject panel to buckle at the design 
load, the effective thickness for use in computing section properties may be taken as 

approximately t \ —-\ ( — Y defined in figure 3-24. If it remains unbuckled the cor- 
\Fj\yJ , E \ 

responding effective thickness may be taken as t yj^ J. The applicable procedure must 

be checked by computing the actual stress in the plating and comparing it with F Ccr . 
The resultant external applied loads on the section in question should be resolved into : 

(1) Vertical shear (in plane of symmetry). 

(2) Transverse shear (at reference point determined by fig. 3-23). 

(3) Moment about each of the principal section axes. 

(4) Torque about reference axis (for example, the intersection with the plane of 
symmetry of the transverse reference axis defined by fig. 3-23). 

The plywood panels (sides, top, and bottom) can be considered to carry the shear upon 
the section, both that due to the vertical and transverse loads and that resulting from 
torsion. When the flange material is concentrated in the longerons, the shear intensity 
(pounds per inch run) can be considered constant between adjacent flanges. The shear 
intensity, and thus the shear stress, may then be determined by figure 3-23 without 
the use of the shear center. Such center may be determined, if desired, by the methods 
of reference 3-11. Calculations made in connection with the application of the thin-shell 
theory, developed primarily for use with isotropic metal materials, should be modified 
to account for variations in the modulus of rigidity (G) for the various wood panels as 
affected by wood species, direction of grain, relative thickness and arrangement of plies, 
according to the methods described in chapter 2. 

If the shell thickness, curvature, and frame spacing are such that the buckling 
stresses will not be exceeded under conditions of maximum oading, the section properties 
may be calculated usfhg the full shell area as modified to correspond to equivalent 
longeron material, that is, the proportionate amount of effective shell material, in terms 

E 

of longeron material, is equal to — as previously described. When the section prop. 

E, 

erties are thus calculated on the basis of longeron material, the bending stress in the 
longerons is determined in the usual manner. 

U=^ (3:59) 

Where yi is the distance of the longeron material from the neutral axis. The bending 
stress in the plywood material, however, is determined as 

(3:60) 

Where yi is the distance of the subject material from the neutral axis. 

The possible variety of assumptions made to facilitate analysis can be considerable 
and will, to a large extent, be determined by the individual details of the problem 
together with the designer's experience, judgment, and discretion. An adequate sup- 



METHODS OF STRUCTURAL ANALYSIS 



191 



plementary static-test program is required, and it is also essential that the assumptions 
used in converting the test data into allowable loads and stresses be duplicated in the 
stress analysis of the flight article. 

3.42. Reinforced-Shell Type. This type of construction is very broad in nature 
and covers the field extending from the longeron type with large longerons and thin 
shell to the type approaching the pure shell, that is, small longitudinals and thick shell. 

3.421. Stressed-skin fuselages. Stressed-skin fuselages usually are structures of 
the reinforced-shell, single-cell type, and the basic methods of wing analysis, as described 
in section 3.13 generally can be applied directly to the analysis of such fuselage struc- 
tures. Due to variations of the type of loading and certain other structural problems, 
however, it is considered advisable to review the fuselage analysis problem as a separate 
subject. 

Unless a fuselage of this nature conforms closely to a previously-constructed type, 
the strength of which has been determined by test, a stress analysis is not considered 
as a sufficiently accurate means of determining its strength. The stress analysis should 
be supplemented by pertinent test data. Whenever possible, it is desirable to test 
the entire fuselage for bending and torsion, but tests of certain component parts may 
be acceptable in conjunction with a stress analysis. 

3.422. Computation of bending stresses. Prior to computing the bending stresses, 
it is necessary to compute the fuselage-section properties. As was previously recom- 
mended in section 3.13, it is considered advisable to make a sketch of the fuselage 
section considered. This sketch should indicate all of the material assumed to be 
effective. Figure 3-25 is a sketch of a fuselage cross section of the subject type. 

On the tension side of the fuselage the skin material may be assumed to be acting 
as discussed in the following, while, on the compression side, only the effective width 
of skin (section 2.76) adjacent to the stiffener should be assumed to be acting. In 
general, the modulus of elasticity of the plywood plating will differ from that of the 
stiffener material. Account of this fact must be taken in calculating the section prop- 
erties. This may be done by converting the actual area of the plating on the tension 
side into that of equivalent stiffener material, either in terms of equivalent thickness 
or equivalent widths — the latter being somewhat analogous to the effective width as 
used on the compression side. The geometrical shape of the section contour together 
with the arrangement and spacing of stiffener material will dictate which method of 
treatment is analytically simpler or more accurate. The proportionate effectiveness of 

E, 

the plating material in tension may be taken as — as described previously under 
section 3.42. E * 

Proper account for wood species, plywood grain attitude and arrangement, and 
veneer thicknesses should be taken into account according to the procedures described 

under section 2.76. The determination of bending stresses by means of the formula 

implies the assumption of plane sections remaining plane sections. Hence, the cal- 
culated stresses in the plating material, as based upon section properties determined 
by conversion of plating material into equivalent stiffener material, must also be modified 
E 

in the ratio — . The resulting corrected stresses in the plating must be compared with 



192 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 




ILLUSTRATING TREATMENT OF MATERIAL 
EFFECTIVE IN 3 ENDING A 30UT X-X AXIS 

Figure 3-25. — Reinforced shell fuselage. 

the allowable tensile stresses in the plating material as described in section 3.1383. 
Such a check should always be made of plywood material adjacent to highly stressed 
stiffener material, even where the contribution of such plywood material has been 
completely neglected in the determination of section properties. In order to account 
for the effect of shear on the effective widths for stiffeners on the side of the fuselage, 
it is advisable to compute the effective widths for all stiffeners on the compression side 
on the basis of a panel edge stress corresponding to the allowable stress of the stiffener, 
rather than the actual stress to which it may be subjected. It is customary to assign 
to each stiffener and adjacent skin an item number. Prior to actual computations, the 
designer should make an estimate of the neutral axis location, thereby dividing the 
elements into those on the compression side and those on the tension side. After the 
location of the true centroid of the section has been determined, the designer will be 
able to check the accuracy of his original assumptions as to neutral-axis location. 

It usually will be found that no corrections for axis location are necessary if the 
final axis is located relatively close to the one originally assumed. A procedure similar to 
that described in section 3.1330 will be found convenient for computing the section 
properties. Distances and moments originally are taken from some conveniently lo- 
cated reference axis. The sum of moments about the reference axis, after being divided 
by the sum of the areas in the section, gives the location of the neutral axis of the sec- 



METHODS OF STRUCTURAL ANALYSIS 



193 



tion. Distances of the items from the neutral axis are then determined. The sum of 
the products of the areas located on either side of the neutral axis multiplied by the 
distances to the neutral axis is equal to the static moment of the section about the neutral 
axis, Q, and the sum of second moments of all of the elements of the section is equal to 
the moment of inertia of the section, I. Where the axial loads produce appreciable 
values of bending moments on the fuselage, these moments should be included in the 
bending moment, M, which is used to obtain the axial stresses due to bending. 

Critical stresses commonly are assumed to occur at the stiff eners located farthest 
away from the neutral axis on the compressive side, and the stresses in these stiffeners 

resulting from bending are computed by the equation, M being the critical moment 

at the section and y being the distance of the stiffener from the neutral axis. 

Although the bending theory indicates that the outermost fibers are the critical 
ones, it will often be found that stiffeners located near the top or bottom, on the shoulders 
of the section, are the ones which are liable to fail during tests if the skin buckles in 
shear. Such stiffeners usually are subjected to comparatively large direct stresses due 
to bending and, at the same time, may act as the stiffeners of the tension-field shear 
material transmitting the shearing stresses to the outermost stiffeners. Unless these 
stiffeners are of sufficiently large proportions to resist the bending loads imposed by 
the tension-field effects, failures of these stiffeners may occur at loads smaller than 
anticipated. 

3.42 3. Computation of shearing stresses. The bending material in fuselage 
sections usually is distributed in such a manner that under symmetrical loadings it 
may be safely assumed that each side carries half of the vertical shear load, and the cor- 

. . VQ 

responding shearing stress, f s , at any point is equal to , where V = the shear force act- 

2tl 

ing on the section, Q = static moment about the neutral axis of the areas located between 
the outermost fibers and a horizontal line through the point under consideration, / = 
moment of inertia of the section, and / = thickness of the skin at the point under con- 
sideration. 

The sum value, Qx (table 3-5), should be used for determining the maximum 
shearing stresses that occur at the neutral axis of the fuselage. Although these methods 
pertain to the analysis of the fuselage for a shear load applied in a vertical direction, 
similar methods can be employed for a shear load applied horizontally, such as a side 
load on the vertical tail. If the structure is not too unsymmetrical about a horizontal 
plane, the shear center for application of the horizontal load may be estimated, using 
overlapping assumptions. If a more exact solution of shear distribution is desired, 
the methods of section 3.135 may be used. The total shear stress (or intensity) at any 
section is that obtained from the superposition of the component shear stresses (or 
intensities) resulting from vertical loads, transverse loads, and torsion. 

Although the fuselage structure as a whole should be checked for the shear distribu- 
tion as determined in the foregoing, it is recommended that certain sections of the 
fuselage be checked for other types of shear stress distribution that may be more in line 
with the actual load application. At the point of wing attachment to the fuselage, for 
example, very large loads are transmitted to the fuselage frame through the attachment 



194 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



fitting. It is reasonable to assume that high shearing stresses will be present near this 
fitting, gradually tapering to the extremity of the frame. Although this assumption is 
not in agreement with the conventional bending theory, it is recommended that it be 
considered in design to allow for probable shear concentrations. 

T 

Torsional shear stresses can be computed by the conventional formula /„ = 

%A t 

and should be combined with the stresses due to direct shear. The tendency of tension 
fields to sag the stiffeners also should be considered. Because similarity seldom exists 
between the geometric properties of different airplane structures, it is difficult to draw 
conclusions from one design as to the allowable shear stresses to be used for other 
designs. It is usually necessary, therefore, to conduct panel tests on representative curved 
shear panels. 

3.43. Pure-Shell Type. By definition, the pure shell or monocoque type of structure 
incorporates no longitudinal stiffening members. Hence, the ultimate strength of such a 
structure may be taken as the critical buckling strength of its elements. As described 
in chapter 2, the buckling strength of a plywood panel may be estimated from its thick- 
ness, frame or stiffener spacing, wood species, arrangement of plies, and curvature. 
It is generally desirable that no portion of the structure become buckled prior to the 
application of the design load. In such a case, in. the calculation of section properties, 
the material may be considered fully effective and the stresses determined according 
to the fundamentals of mechanics. 

In a section such as shown in figure 3-26B, however, certain portions may become 
buckled at low loads without materially affecting the final load-carrying capacity of the 
total section. This may be exemplified by the buckling of flat panels on the compres- 
sion side while the major portion of the total flange material is unbuckled by reason 
of its difference in curvature or thickness. It is generally satisfactorily conservative 
to omit the buckled material from consideration. Such, a partially buckled structure 
must, of course, be adequately stiffened by frames. 

3.431. Monocoque-shell fuselages. The basic principles of the design of thin- 
walled cylinders, as discussed in ANC-5 sections 1.63 and 1.64 can be applied to the 
design of monocoque fuselages. The monocoque portion of the fuselage structure usually 
is restricted to certain sections of the fuselage, such as the tail portion. In the center 
and in the forward portions of the fuselage, the reinforced-shell type of construction, 
which is more suited to the region where cut-outs are present, generally is used. Careful 
attention should be given to that part of the fuselage structure where two types of con- 
struction join. Adequate length and attachment of the reinforcing members to the shell 
should be provided. At the points where the monocoque section stops at cut-outs, 
transfer of the load from monocoque portion to the stiffeners around the cut-out should 
be investigated carefully. (Ref . 3-19. ) 

Tests of monocoque fuselages have demonstrated that the strength is dependent 
to some extent on the smoothness of the plating. The designer should, therefore, be 
certain that the methods of assembly of monocoque fuselages in the shop will produce 
a satisfactory product. Where small margins of safety are present and when the effects of 
load concentrations have not been taken into account conservatively, strength tests 
should be carried to the full ultimate-load values, because the type of failure in this 
type of structure usually is elastic, and the appearance of the structure under proof 



METHODS OF STRUCTURAL ANALYSIS 



195 




Y 

A. UNBUCKLED (FULLY EFFECTIVE) 

UNBUCKLED 




B. PARTIALLY BUCKLED 

Figure 3-26. — Pure shell-type fuselage. 

load may be no indication of the ability of the structure to carry the required ultimate 
loads. 

3.44. Miscellaneous Fuselage Analysis Problems. Each new type of fuselage 
may present a new set of problems which has not occurred in other types. It is recom- 




196 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



mended, therefore, that every new type of fuselage be tested at least to the critical ulti- 
mate loads to determine the presence of possible stress concentrations and other effects 
which could have been overlooked in the most careful design. Some of the analysis 
problems which are somewhat common to all types of fuselages are discussed in the fol- 
lowing sections. 

3.441. Analysis of seams. The allowable loads of the seams should be computed 

and compared with the loads imposed by direct tensile stresses, by shear stresses, by any 
tension field effects of the shear stresses, and by combined stresses due to the action of 
all these stresses. 

3.442. Analysis of frames and rings. The analysis of the fuselage frames consti- 
tutes a separate problem. Many manufacturers have adopted certain standard methods 
of frame analysis, which, although not necessarily mathematically rigorous for the types 
of the structures considered, have produced satisfactory designs. A general discussion 
of some of these methods is given. 

3.4421. Main frames. Main frames are primarily for the purpose of distributing 
into the fuselage such concentrated loads as the loads from wings, tail surfaces, or 
landing gear, and those resulting from the local support of items of mass. Main-frame 
structures usually are of the redundant type and their analysis is based on the principles 
of least work and related or equivalent methods such as strain energy, column analogy, 
moment distribution, or joint relaxation (ref. 3-2 and 3-3). 

Figures 3-27 A, B, and C show a fuselage main frame under a symmetrical loading 
condition. The loads from the wing (or landing gear) are shown applied at the applicable 
fittings and are resisted by shear forces in the fuselage skin. To agree with the elementary 
bending theory, these shear intensities should be distributed so as to conform to the 

or — values of the fuselage section, as applicable, giving a distribution of shear 

forces of the type shown in figure 3-27 A or B. Some designers take into account the 
fact that, due to concentration of load where the frame is attached to the wing, the shear 
is carried mostly by the adjacent fuselage skin and the shear resistance of the skin is 
reduced arbitrarily, somewhat in proportion to its distance from the point of concentrated 
load application. This would yield a shear force distribution of the type shown in figure 
3-27 C. In such cases, the fuselage skin should also be checked for the high stresses 
indicated. 

The ordinary method of frame analysis is strictly applicable to frames the de- 
flections of which are not restricted by the fuselage skin. Actually, the frame deflections 
may become quite pronounced and the outward deflections are resisted by double- 
curvature effects in the fuselage skin or by the support of adjacent frames. This action 
of the skin is equivalent to an introduction of inward-acting loads resisting the frame 
bending and hence to a reduction of frame stresses to smaller values than those indicated 
by an analysis based upon shear distributions as described. The present development of 
the theory does not indicate quantitatively just what allowance can be made for this 
reduction of stresses. It is recommended, therefore, that the frame analysis be conducted 
by the methods similar to the ones indicated. 

Where relatively deep frames are used, the moments induced by the wing de- 
flections may become important and should, therefore, be analyzed. 



METHODS OF STRUCTURAL ANALYSIS 



197 




ft: * ^ IS »U 



<v ^ cj 5 >*- ^ 

^ * 9c 

=c o ^ 

5r ^ ^ 



<m y> ^ 



— 



198 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



3.4422. Intermediate frames. Intermediate frames are provided to preserve the 
shape of the fuselage structure, to reduce the column length of the stiffeners, and 
to prevent failure of the structure due to general instability. They are subjected to 
several types of loading; such as, those due to tension fields in the skin, to fuselage 
bending, to transfer of shear to the fuselage plating. Many of these loads are compara- 
tively small and often tend to balance each other. For these reasons the design of 
intermediate frames is often based on the experience of the designer or on semiempirical 
methods. In the case of large airplanes, however, it becomes of considerable importance 
to design frames of this type to provide suitable stiffness for the prevention of general 
instability. 

3.443. Effects of cut-outs. Effects of cut-outs usually are allowed for by omitting 
the bending material affected by the cut-out from the computation of the section prop- 
erties. For shearing stress computations in the location of regularly spaced cut-outs, 
such as windows, the shear stress in the skin between cut-outs may be taken as equal 
to that computed on the assumption that no cut-outs are present and then increasing 
this value by the ratio of distance between cut-out centerlines to the distance between 
the cut-outs. Such treatment, although quite arbitrary, has served satisfactorily with 
metal material. Because of the inherent lack of ductility in wood and its inability to 
deform plastically and redistribute stresses adjacent to local concentrations such as 
cut-outs, the incorporation of large calculated margins of safety is recommended in such 
locations. 

In case of large openings, such as the cabin door cut-outs, allowance for bending 
stress redistribution usually is made by modifying the section properties by omitting the 
material affected by the cut-out. For computation of the shearing stresses, it may be 
assumed that the direct shear load is carried through that side of the fuselage not con- 
taining the cut-out. The couple resulting from this unsymmetrical reaction in way 
of the cut-out can be assumed to be resisted by a shear couple consisting of equal and 
oppositely directed transverse reactions in the top and the bottom of the fuselage. The 
redistribution of the shear stress, as assumed, can be achieved best if bulkheads are 
provided on both sides of the door. Where only one main bulkhead is provided (at 
only one end of the cut-out ) shear redistribution on the other side of the cut-out must 
be accomplished by the frame under the flooring and by the intermediate frames. Refer- 
ence 3-19 describes the basic theory and recommended methods of determining the 
shear distribution in the plating about cut-outs, and also the corresponding effect of the 
cut-outs upon the loads in the stringers and frames. 

3.444. Secondary structures within the fuselage. Often the designer is faced with 
the problem of existence of a secondary beam structure inside the main fuselage or hull 
structure. This secondary structure may consist of keels or keelsons in a flying-boat hull, 
or of the floor supporting structure or nose-wheel retracting tunnel in a fuselage. If this 
type of structure is analyzed separately under the specified local loads alone, the stress 
distribution may not correspond to the distribution that will be obtained with it acting 
in conjunction with the rest of the fuselage structure. The designer should make certain 
that the combined effects of the two structures are in agreement and that the action of 
the structure as a whole is consistent with expected deformations. 

3.45. Strength Determination. The strength of the structure is determined by 
comparison of the calculated internal loads and stresses with the allowables obtained 



METHODS OF STRUCTURAL ANALYSIS 



199 



either from tests or from the information given in chapter 2. The determination of the 
strength of shell structures, including reinforced shells, is presented in detail in section 
3.138. 

3.5 HULLS AND FLOATS. The analysis of hulls and floats may be treated in a 
manner similar to that used with fuselage structures, the chief difference being in the 
manner in which the major external loads are applied, that is, by direct contact with 
the water in the form of normal pressures. Fundamentally, hull and float structures 
consist of : 

(1) Bottom plating — that, in contact with the water, is loaded by the normal pres- 
sures developed in landing, take-off, or buoyancy, and transfers such loads to the — 

(2) Bottom stringers — that support the plating and transfer the plating loading 
to the supporting — 

(3 ) Frames — that in turn carry the water loads through to the — 

(4) Main longitudinal girder — or general structure. Consideration is given to the 
fact that water causes concentrated local loads on float and hull bottoms that may 
reach intensities considerably above the average loading and may be applied at different 
times and for different durations to different portions of the bottom structure. For 
these reasons the strength requirements for design of the bottom plating are specified 
as more severe than those for stringer design. The bottom stringer strength require- 
ments are, in turn, more severe than those for complete frame design. The specified 
loads as applicable to the design of the general structure are in general of lesser local 
intensities but are consistent with the design airplane accelerations and total reactions. 

3.51. Main Longitudinal Girder. This structure may consist of a centerline truss 
or bulkhead girder to which the frames, deck, side and bottom plating are attached. 
Or, the deck, side, and bottom plating and stringers plus other longitudinal material 
connecting to, and capable of acting with, the skin plating and stringers may be con- 
sidered as a reinforced shell which comprises the longitudinal girder. In such a structure 
the frames not only serve to transmit the water loads to the general structure, but pro- 
vide the transverse and circumferential stiffening for the shell. The effective longitudinal 
members ordinarily considered to take the bending loads consist of: keel, bottom string- 
ers, keelson, chine, deck, and stiffeners. The effective shear material consists of side, 
deck, and bottom plating. The analysis assumptions, calculation of section properties, 
and determination of normal and shearing stresses applicable to the longitudinal girders 
are in general as described under section 3.4 for fuselage analysis. 

3.52. Bottom Plating. Thin plating, when subjected to sufficient normal pressures 
will either rupture or deflect excessively and take a permanent set. In hulls and floats 
this latter effect is known as "wash boarding," and in an acceptable structure should not 
be allowed to occur at loads below those corresponding to yield-point loads. For this 
reason the design criteria established by the procuring or certificating agency in general 
consists of specification of certain design-bottom-pressure loadings in conjunction with 
the permissible permanent deformations at the specified pressure loadings. Permanent- 
deformation is measured at the center of the plating panel, between stringers and relative 
to the stringers, in a direction normal to the plane of the plating. 

The analytical determination of bottom-plating stresses and deflections is exceed- 
ingly difficult of accurate attainment, and the problem of design calculation methods, 
including the basis for allowable stresses, hence lends itself most readily to treatment by 



200 



ANC BULLETIN— DESIGN OE WOOD AIRCRAFT STRUCTURES 



testing procedures. Test panels representative of (1) the plating species, thickness and 
plywood type, (2) the stringer spacing, frame spacing, and panel aspect ratio, and (3) 
method of edge support and type of edge restraint should be tested under normal pres- 
sures, and the applicable strength criteria (ultimate strength, arbitrary or true yield, 
and permanent deformation) determined. Test data may be interpreted and converted 
in light of the calculation procedures described in chapter 2. 

In such a treatment, two of the influential factors that determine the calculated 
stresses and deflections are (1) type of edge support, and (2) aspect ratio of panel. 
Clamped or fixed edges assume the plating to be restrained from any rotation at the 
edges, the neutral plane of the plywood maintaining zero slope. In simply supported 
edges, conversely, a possibility of rotation of the neutral plane of the plywood at the 
edge is implied. The plates actually encountered in the design of floats and hulls lie 
somewhere between fixed and supported edges and may be considered as elastically 
restrained. The maximum stress in a plate with fixed edges occurs at the long edges, 
whereas it occurs in the middle of a plate with simply supported edges. It follows from 
this that a slight deflection or twist of the fixed edges of a plate will decrease the stress 
close to the edges where it is a maximum and increase it near the middle where it was, 
however, originally much less. Bottom stringers are not ordinarily very stiff torsionally 
and constitute a type of support bordering upon the simply supported edge. On the 
other hand, keel, keelson, and chine members are necessarily quite stiff torsionally, as 
well as laterally, in that they must be well gusseted to adjacent frames and, forming 
the edge of the plate panels, must be stiff enough to prevent lateral deflections. Hence, 
the analytical treatment under both limiting conditions of edge support should give 
considerable guidance in design. 

The ratio of frame spacing to stringer spacing ordinarily exceeds 3.0 and hence, the 
aspect ratio of the plating panels for use in design can usually be taken as infinite. 

3.5 3. Bottom Stringers. As previously mentioned, the bottom stringers serve to 
transfer the bottom plating normal loads to the transverse frames. They may be con- 
sidered in general as continuous beams supported at the frames with a running load per 
unit of length equal to the stringer spacing times the intensity of bottom pressure. 
Under the ordinary conditions of uniform pressure, frame and stringer spacings, the 
symmetry of loading would permit the consideration of the stringer as a uniformly loaded 
continuous beam over fixed supports. This would lead to a design bending moment in 
the stringer: 



where W = stringer transverse loading, in pounds per inch 

and L = support spacing, in inches. 
The extreme probability of loadings other than symmetrical and the finitely elastic 
nature of the support restraint leads to the use of the more conservative specification 
of the design bending moment as : 




(3:61) 



10 



(3:62) 



When the conditions of loading are definitely different from these assumptions (that is, 
when the pressure varies, when the stringer is not continuous, or when the support has 



METHODS OF STRUCTURAL ANALYSIS 



201 



unusual restraint characteristics) the stringer should of course, be designed to the local 
conditions specifically applicable. 

It is rational to consider a portion of the plating adjacent to a stringer as effectively 
contributing to the section properties of the stringer. It is important that the same 
assumptions as to plating effectiveness be used in converting test data into allowable 
stresses as is used in the analysis of the flight article under the specified loads. 

As well as being analyzed for the specified design bottom-pressure loading, the 
plating and stringer combination should be checked for the conditions in which it is 
both subjected to direct water loads and also forms a part of the effective flange material 
of the general longitudinal girder structure. In such conditions, the stresses resulting 
from the bottom pressures consistent with the loadings on the general structure are 
superimposed upon the stresses incurred as a portion of the flanges of the general structure. 

3.54. Frames. Hull and float frame design differs from ordinary fuselage frame 
design principally in the nature of the applied loads which result from direct water 
pressures. Each frame is considered to take the bottom loadings applied to the plating 
and stringer combination structure in the area adjacent to the frame. Such loaded area 
extends approximately one-half of the frame spacing to both sides. The bottom loads 
are usually transmitted from the stringers directly to the frame in the area between the 
chines. The assumptions as to the nature and magnitude of the balancing reactions in 
the form of shear in the side and deck plating may be patterned after those used in 
fuselage frame design. 

In almost all instances, frame analysis involves the problem of the application of 
the fundamental methods of least work and in this respect may be treated in a manner 
similar to that employed with analogous fuselage frames. The probability of unsym- 
metrical loading applications on V-bottom hulls and floats in take-off and landing is 
quite high. For this reason the procuring or certificating agency specifies in all instances 
certain unsymmetrical design-loading conditions. Such loading conditions are often 
critical for the design of frames, and hence the analysis of frames loaded in this manner 
should be given the utmost care and consideration. 

3.5 5. Strength Determination. The strength of the structure is determined by 
comparison of the calculated internal loads and stresses with the allowables obtained 
either from tests or from the information given in chapter 2. The determination of the 
strength of shell structures, including reinforced shells, is presented in detail in section 
3.138. 

3.6. MISCELLANEOUS. Treatment of the wing, fuselage, hull, tail, and control 
surfaces does not complete the stress analysis of the airplane structure. In airplanes of 
wood construction, however, it is considered that these same structural components 
constitute nearly all of those in which the use of wood is significant and in the analysis 
of which the physical properties of wood will enter as an important factor. Hence, for 
such reasons and as explained in section 3.00, treatment of the detailed analysis problems 
related to the remaining important airplane structural components will not be included 
herein. Such components would include, for example, landing gear, engine mount, con- 
trol systems, fittings, and joints. The determination of the design load applied to each 
individual wood structural element of a joint (mechanical joint or glue joint), or fitting 
attachment, may be determined by basic principles of mechanics and machine design. 
Where it would significantly affect the distribution of the design load, the nonisotropic 



202 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



nature of wood, which results in the strength and elastic characteristics being dependent 
upon the relation between the directions of the load and of the grain, should be taken 
into account by a rational treatment or provided for by conservative arbitrary assump- 
tions. The design load thus determined for such an element should be compared with 
the allowable load defined by the applicable portions of chapter 2 (principally section 
2.9). The designer is referred, in general, to the many existing tests, technical papers, 
and publications which adequately handle such miscellaneous analysis problems. 



METHODS OF STRUCTURAL ANALYSIS 



203 



REFERENCES FOR CHAPTER 3 

(3-1) Akerman, J. D. and Stephens, B. C. 

1938. POLAR DIAGRAMS FOR SOLUTION OF AXIALLY LOADED BEAMS. Jour. Aero. Sci. July,1938 

(3-2) Cross, Hardy 

1930. the column analogy. Univ. of Illinois Eng. Exp. Sta. Bulletin 215. 
(3-3) 

1930. analysis of continuous frames by distributing fixed-end moments. Proc. 
A.S.C.E. May, 1930. 
(3-4) Erlandsen, O. and Mead, L. 

1942. a method of shear-lag analysis of box beams for axial stresses, shear stresses, 
and shear center. N.A.C.A. Advance Restricted Report. 
(3-5) Hatcher, Robert S. 

1937. rational shear analysis of box girders. Jour. Aero. Sci. April, 1937. 
(3-6) Ebner, Hans 

1934. torsional stresses in box beams with cross sections partially restrained 
against warping. N.A.C.A. Tech. Memo. 744. 

(3-7) Kuhn, Paul 

1935. ANALYSIS of two-spar CANTILEVER wings with SPECIAL REFERENCE TO TORSION 
and load transference. N.A.C.A. Tech. Rept. 508. 

(3-8) Kuhn, Paul 

1935. bending stresses due to torsion in cantilver box beams. n.a.c.a. tech. 
Note 530. 
(3-9) 



1938. APPROXIMATE STRESS ANALYSIS OF MULTI-STRINGER BEAMS WITH SHEAR DEFORMA- 
TION of the flanges. N.A.C.A. Tech. Rept. 636. 



1939. loads imposed on intermediate frames of stiffened shells. N.A.C.A. Tech. 
Note 687. 



1939. SOME elementary principles of shell stress analysis with notes on the use 
of the shear center. N.A.C.A. Tech. Note 691. 



(3-10) 
(3-11) 
(3-12) 

1942. a method of calculating bending stresses due to torsion. N.A.C.A. Advanced 
Technical Report. (Restricted) 
(3-13) Kuhn, P. and Chiarito, P. 

1941. lag in box beams, methods of analysis and experimental investigations. 
N.A.C.A. Tech. Note 739. (Restricted) 

(3-14) LUNDQUIST, E. AND SCHWARTZ, E. B. 

1942. A STUDY' OF GENERAL INSTABILITY OF BOX BEAMS WITH TRUSS TYPE RIBS. N.A.C.A. 

Tech. Note 866. (Restricted) 
(3-15) Niles, A. S. and Newell, J. S. 

1938. airplane structures. Second edition John Wiley and Sons, Inc. 
(3-16) Rowe, C. J. 

1924. application of the method OF least WORK TO redundant structures. A.C.I.C. 
495. 

(3-17) Schwartz, A. M. and Bogert, R. 

1935. ANALYSIS OF A STRUT WITH A SINGLE ELASTIC SUPPORT IN THE SPAN, WITH APPLICA- 
TIONS TO THE DESIGN OF AIRPLANE JURY'-STRUT SYSTEMS. N.A.C.A. Tech. Note 529. 

(3-18) Shanley, P. R. and Cozzone, F. P. 

1941. unit method of beam analysis. Jour. Aero. Sci. April, 1941. 
(3-19) Wagner, H. 

1937. THE stress distribution in shell bodies and wings as an equilibrium problem. 
N.A.C.A. Tech. Memo. 817. 



204 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



CHAPTER 4. DETAIL STRUCTURAL DESIGN 

TABLE OF CONTENTS 



4.0 GENERAL 205 

4.00 Introduction 205 

4.01 Definitions 205 

4.010 Solid Wood 205 

4.011 Laminated Wood 205 

4.012 Plywood 205 

4.013 High-density material 205 

4.1 PLYWOOD COVERING 205 

4.10 General 205 

4.11 Joints in the Covering 205 

4.12 Taper in Thicknessof the Covering .206 

4.13 Behavior Under Tension Loads . .208 

4.14 Behavior Under Shear Loads 208 

4. 1 5 Plywood Panel Size 209 

4.16 Cut-Outs 210 

4.2 BEAMS 210 

4.20 Types of Beams 210 

4.21 Laminating of Beams and Beam 

Flanges 213 

4.22 Shear Webs 213 

4.23 Beam Stiffeners 213 

4.24 Blocking 215 

4.25 Scarf Joints in Beams 215 

4.26 Reinforcement of Sloping Grain . .215 

4.3 RIBS 216 

4.30 Types of Ribs 216 

4.31 Special Purpose Ribs 216 

4.32 Attachment of Ribs to the 

Structure 218 

4.4 FRAMES AND BULKHEADS 220 

4.40 Types of Frames and Bulkheads. . 220 

4.41 Glue Area for Attachment of 

Plywood Covering 220 

4.42 Reinforcement for Concentrated 

Loads 220 



4.5 STIFFENERS 220 

4.50 General 220 

4.51 Attachment of Stringers 222 

4.52 Attachment of Intercostals 222 

4.6 GLUE JOINTS 222 

4.60 General 222 

4.61 Eccentricities 222 

4.62 Avoidance of End-Grain Joints. . .223 

4.63 Gluing of Plywood Over Wood- 

Plywood Combinations 224 

4.64 Glui ng of High Density Material .224 

4.7 MECHANICAL JOINTS 224 

4.70 General 224 

4.71 Use of Bushings 224 

4.72 Use of High Density Material 224 

4.73 Mechanical Attachment of Ribs. .226 

4.74 Attachment of Various Types of 

Fittings 226 

4.75 Use of Wood Screws, Rivets, Nails, 

and Self-Locking Nuts 226 

4.8 MISCELLANEOUS DESIGN 
DETAILS 227 

4.80 Metal to Wood Connections 227 

4.81 Stress Concentrations 227 

4.82 Behavior of Dissimilar Materials 

Working Together 228 

4.83 Effects of Shrinkage 228 

4.84 Drainage and Ventilation 229 

4.85 Internal Finishing 230 

4.86 External Finishing 231 

4.87 Selection of Species 232 

4.88 Use of Standard Plywood 232 

4.89 Tests 233 

4.9 EXAMPLES OF ACTUAL DESIGN 
DETAILS 233 



DETAIL STRUCTURAL DESIGN 



4.0. GENERAL. 

4.00. Introduction. Detail design practice is constantly changing and current 
good practice may at any time be obsoleted by some new treatment of a particular 
design problem. Therefore, the examples presented on the following pages represent 
only the current methods used in handling problems of design details. It should be 
remembered, however, that many of these methods have withstood the test of time, 
having been used since the first introduction of wood aircraft. 

4.01. Definitions. The following definitions explain a few general terms which are 
sometimes confused by the wood aircraft designer. Other terms requiring definition 
are explained as they appear in the text. 

4.010. Solid Wood. Solid wood or the adejctive "solid" used with such nouns as 
beam or spar refers to a member consisting of one piece of wood. 

4.011. Laminated Wood. Laminated wood is an assembly of two or more layers 
of wood which have been glued together with the grain of all layers or laminations 
approximately parallel. 

4.012. Plywood. Plywood is an assembled product of wood and glue that is 
usually made of an odd number of thin plies (veneers) with the grain of each layer at an 
angle of 90° with the adjacent ply or plies. 

4.013. High-Density Material. The term "high density material" as used through- 
out this chapter includes compreg or similar commercial products, heat stabilized wood, 
or any of the hardwood plywoods commonly used as bearing or reinforcement plates. 

4.1 PLYWOOD COVERING. 

4.10. General. Nearly all wood aircraft structures are covered with stressed ply- 
wood skin. The notable exceptions are control surfaces and the rear portion of lightly 
loaded wings. Shear stresses are almost always resisted by plywood skin, and in many 
cases, a portion of the bending and normal loads is also resisted by the plywood. 

4.1 1. Joints in the Covering. Lap, butt, and scarf joints are used for plywood skin. 
When plywood joints are made over relatively large wood members, such as beam 

flanges, it is desirable to use splice plates, often called aprons or apron strips, regardless 
of the type of joint. It is desirable to extend the splice plates beyond the edges of the 
flange so that the stress in the skin will be lowered gradually, thus reducing the effect 
of the stress concentration at this point. Splice plates (fig. 4-1) can be made to do 
double duty if they are scalloped corresponding to rib locations so that they- may act as 
gussets for the attachment of the ribs. 

Scarf joints are the most satisfactory type and should be used whenever possible. 
Scarf splices in plywood sheets should be made with a scarf slope not steeper than 1 
in 12 (fig. 4-2). Some manufacturers prefer to make scarf joints in such a way that the 
external feather edge of the scarf faces aft in order to avoid any possibility of the air- 
flow opening the joint. 



205 



206 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




Figure 4-1. — Use of Splice Plate. 




Acceptable Better 

Scarf Joint Made Directly Upon Scarf Joint Made 

Solid or Laminated Flange Upon Splice Plate 

Figure 4-2. — Scarf Splices. 



If butt joints (fig. 4-3) are made directly over solid or laminated wood members, 
as over a spar or spar flange, experience has indicated that there is a tendency to cause 
splitting of the spar or spar flange at the butt joint under relatively low stresses. A 
similar tendency toward cleavage exists where a plywood skin terminates over the 
middle of a wood member instead of at its far edge. 

Lap joints (fig. 4-4) are not recommended because of the eccentric load placed 
upon the glue line. If this type is used it should be made parallel to the direction of 
airflow, only, for obvious aerodynamic reasons. 

4.12. Taper In Thickness of the Covering. Loads in the plywood covering usually 
vary from section to section. When this is so, structural efficiency may be increased by 
tapering the plywood skin in thickness so that the strength varies with the load as closely 
as possible (fig. 4-5). To taper plywood in thickness, plies should be added as dictated 



DETAIL STRUCTURAL DESIGN 



207 



POOR POOR BETTER 




SKIN TERMINATES AT THE BUTT JOINT DIRECTLY OVER SPLICE PLATE 15 GLUED TO 

MIDDLE OF THE FLANGE . SOLID OR LAMINATED WOOD THE FLANGE AND THE BUTT 

HA5 SAME EFFECT A5"A" JOINT 15 MADE ONTOP OF IT 

Figure 4-3. — Butt Splices. 




A-A B-B 

Plan View of Wing Panel Lap Joint on a Rib at a Lap Joint Where It 

Chordwlse Station Between Beams Croesee Beam Flange 



Figure 4-4. — Lap Splices. 



by increasing loads. In doing so, the plywood should always remain symmetrical. For 
example, plywood constructed of an odd number of plies of equal thickness can be 
tapered, and at the same time maintain its symmetry, by adding two plies at a time. 
This method is suitable for bag molding construction. Stress concentrations should be 
avoided by making the change in thickness gradual, either by feathering or by scalloping. 
In bag molding construction, the additional plies are often added internally so that the 
face and back are continuous. 



By Feathering 



By Soalloping 




Figure 4-5. — Tapering Plywood in Thickness. 



208 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



When flat plywood is used, the usual method of tapering skin thickness is to splice 
two standard plywood sheets of different thicknesses at an appropriate rib station 
with a slope of scarf not steeper than 1 in 12 as shown in figure 4-6. 




Figure 4-6. — Scarfing Plywood of Different Thicknesses. 



4.13. Behavior Under Tension Loads. Because the proportional limit in tension 
and the ultimate tensile strength of wood are reached at approximately the same time, 
plywood skin loaded in tension must be designed very carefully. Observation of various 
static test articles has indicated that square-laid plywood (plywood laid so that face 
grain is parallel or perpendicular to the direction of the principal bending stresses) has a 
tendency to rupture in tension before the ultimate strength of the structure has been 
reached (fig. 4-7). Diagonal plywood, however, seldom ruptures before some other 
structural member fails. The reason for this behavior is probably due partly to the fact 
that none of the fibers of the diagonal plywood are in pure tension. The failure under 
tension load at 45° to the grain is almost entirely a shear failure, and the fibers, which 
have a definite yield beyond the proportional limit in shear, may undergo enough in- 
ternal adjustment to permit the plywood to deflect with the structure until some other 
member becomes critically loaded. Square-laid plywood does not yield because some 
of its plies will fail in tension almost immediately after the proportional limit has been 
reached. This drawback of square-laid plywood becomes less important when the skin 
is designed to carry a greater proportion of the bending loads. For the limiting case of a 
shell structure without flanges, square-laid plywood is preferable. 

Rupture of the skin is also influenced by its relative distance from the neutral axis. 
If the beam or beams are located so that part of the skin is appreciably farther from the 
neutral axis than the beam flanges, the skin is more likely to have a premature failure 
than if the flanges are located at the greatest outer fiber distance. Such a condition 
is illustrated by wing spars placed at the 15 and 65 percent chord wise stations of a nor- 
mal airfoil. 

Where the spanwise plies of plywood covering are of a wood species different from 
the beam flanges, it is, of course, desirable that such plies have a ratio of ultimate tensile 
stress to modulus of elasticity equal to or greater than that of the beam flanges. 

4.14. Behavior Under Shear Loads. Diagonal plywood (face grain at 45° angle 
to the edge of the panel) is approximately five times stiff er in shear than square-laid 
plywood and somewhat stronger. When shear strength or stiffness is the controlling 
design consideration, diagonal plywood should be used (sec. 4.22). 



DETAI Jj STRUCTURAL DESIGN 



209 




Figure 4-7. — Static Test Wing Showing Tension Failure of Plywood Covering. 

4.15. Plywood Panel Size. In certain cases the size of plywood panels is dictated 
by the magnitude of directly computable stresses. These occur, for example, in spar 
webs, D-tube nose skin, and fuselage side panels subjected to high shear. In many other 
cases, however, the design loads are insignificant. It then becomes necessary to choose 
combinations of skin thickness and panel size which will stand up under expected handling 
loads, have acceptable appearance, and aerodynamic smoothness. The typical values 
given in table 4-1 have been employed by experienced manufacturers. 



Table 4-1. — Typical panel sizes 



Material 



Thickness 



Panel Size 



Location 



Remarks 



Inch 



Mahogany, yellowpoplar core 

Do 

Do 

Do 

Do 

Do 

Do 

Mahogany 

Do 

Yellowpoplar 



Inch 

12 by 24 maximum 
by 10^ 

10 by 12 
5 by 9 

11 by 20 
10 by II 

24 or 36 square 
7 by 14 
18 by 24 
14 by 36 



Wing skin. 

do 

do. 

Leading edge skin. 
Vertical fin 
Stabilizer 

Fuselage 

Leading edge skin . . . . 

Fuselage 

Wing aft of 50 percent 
chord. 



Spanwise face grain. 



Some curvature required. 
Spanwise face grain. 
Just aft of cabin. 



210 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



4.16. Cut-Outs. When cut-outs are made in plywood skin for windows, inspection 
holes, doors, or other purposes, sharp corners should be avoided, and for all but small 
holes in low-stressed skin, a doubler should be glued to the skin around the cut-out. 
For some types of cut-outs a framework can be installed to carry the shear load and 
doublers need not be used (figs. 4-8, 4-9, and 4-10). 

Doubler 



A-A 





Poor 



Bett»r 



Figure 4-8. — Plywood Cut-Outs. 




Stop Nuts Riveted to Doubler 




Stop Nuts Set in Routed lftood Ring 



X 




Cover Plate 



Section A-A 



Section B-B 



Figure 4-9. — Two Methods of Attaching Inspection Hole Covers. 
4.2. BEAMS. 

4.20. Types of Beams. The types of beams shown in figure 4-11 have been used 
frequently as wing spars, control surface spars, floor beams and wing ribs. The terms 
"beam" and "spar" are often used interchangeably and both are used in this chapter. 

The wood-plywood beams (box-, I-, double I-, and C-) are generally more efficient 
load-carrying members than the plain wood types (plain rectangular and routed). A 
discussion of the relative merits of these various beam types is presented in succeeding 
paragraphs. 

The box beam is often preferred because of its flush faces which allow easy attach- 
ment of ribs (sec. 4.32). The interior of box beams must be finished, drained, and ven- 
tilated. Inspection of interiors is usually difficult. The shear load in a box beam is 




Figure 4-10. — Methods of Carrying Torsion Loads Around Hinge Cut-Outs in Control Surfaces. 



212 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




BOX *T DOUBLET 




*C" PLAIN RECTANGULAR ROUTED 

Figure 4-11. — Types of Beams. 

carried by two plywood webs. By checking shear web allowables by the method given 
in section 2.72, it will be seen that for the same panel size a plywood shear panel half 
the thickness of another will carry less than half the shear load which can be carried 
by the thicker panel. 

The preceding statement points to an outstanding advantage of the I-beam since 
its shear strength is furnished by a single shear web rather than the two webs required 
of a box or double I-beams. Also, the I-beam produces a more efficient connection be- 
tween the web and flange material than the box beam in cases where the web becomes 
buckled before the ultimate load is reached. This is because the clamping action on 
the webs tends to reduce the possibility of the tension component of the buckled web 
cleaving it away from the flange. 

The double I-beam is usually a box beam with external flanges added along that 
portion where the bending moments are greatest. This type allows a given flange area 
to be concentrated farther from the neutral axis than other types. 

The C-beam affords one flush face for the flush type of rib attachment but it is 
unstable under shear loading. C-beams are generally used only as auxiliary wing spars 
or control surface spars. 

Plain rectangular beams are generally used where the saving in weight of the wood- 
plywood types is not great enough to justify the accompanying increase in manufactur- 
ing trouble and cost. This is usually the case for small wing beams, control-surface 
beams, and beams that would require a great deal of blocking. 



DETAIL STRUCTURAL DESIGN 



213 



Routed beams are somewhat lighter than the plain rectangular type for the same 
strength but not so light as wood-plywood types. Usually this small weight saving 
does not justify the increase in fabrication effort and cost. 

In determining the relative efficiency of any beam type, reduction in allowable 
modulus of rupture due to form factors must be considered. 

4.21. Laminating of Beams and Beam Flanges. Beam flanges and plain rectangu- 
lar and routed beams can be either solid or laminated. A detailed discussion of methods 
of laminating beams and beam flanges is presented in section 2.4 of ANC Bulletin 19, 
Wood Aircraft Inspection and Fabrication (ref. 2-4). 

Since the tension strength of a wood member is more adversely affected by any 
type of defect than is any other strength property, it is recommended that all tension 
flanges be laminated in order to minimize the effect of small defects and to avoid the 
possibility of objectionable defects remaining hidden within a solid member of large 
cross section. 

4.22. Shear Webs. Although square-laid plywood has been used extensively as 
shear webs in the past, the present trend is to use diagonal plywood (fig. 4-12) because 
it is the more efficient shear carrying material (sec. 4.14). 



It is desirable to lay all diagonal plywood of an odd number of plies so that the face 
grain is at right angles to the direction of possible shear buckles. In this way the shear 
web will carry appreciably higher buckling and ultimate loads because plywood is much 
stiffer in bending in the direction of the face grain and offers greater resistance to buckling 
if laid with the face grain across the buckles (fig. 4-13). This effect is greatest for 3-ply 
material. 

Figure 4-14 illustrates various methods of splicing shear webs. If the splices are 
not made prior to the assembly of the web to the beam, blocking must be inserted at the 
splice locations to provide adequate backing for the pressure required to obtain a satis- 
factory glue joint. 

4.23. Beam Stiffeners. Shear webs should be reinforced by stiff eners at frequent 
intervals as the shear strength of the web depends partly upon stiffener spacing (fig. 
4-15). In addition to their function of stiffening the shear webs, the ability of beam 
stiffeners to act as flange spreaders is very important and care must be exercised to 
provide a snug fit between the ends of the stiffeners and the beam flanges. External 
stiffeners for box beams are inefficient because of their inability to act as flange spreaders. 

Stiffeners are usually placed at every rib location so that the web will be stiffened 
sufficiently to resist rib-assembly pressures. 




Square-laid Plywood 



Diagonal Plywood 



Figure 4-12. — Types of Shear Webs. 



214 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 




the lace ply of the web ^ 

Figure 4—13. — Orientation of face grain direction of diagonal plywood shear webs. 




Butt Joint with Simple Scarf Joint Diagonal Scarf Joint 

Splice Plate 

Figure 4-14. — Methods of Splicing Shear Webs 





-5tiffener of solid or laminated^ — ladder type stiffener; ^— ply wood web wfth corner 
wood; lightening holes are often wood vertical stiffeners blocks ■, holes are often 
drilled to reduce weight oh the are separated br "plywood cut in web to reduce 
piece may be routed strips weight 

Figure 4-15. — Typical Stiff eners for I and Box Beams. 



DETAIL STRUCTURAL DESIGN 



215 



4.24. Blocking. Any blocking;, introduced for the purpose of carrying fitting loads 
(fig. 4-16), should be tapered as much as possible to avoid stress concentrations. It is 
desirable to include a few cross-banded laminations in all blocking in order to reduce 
the possibility of checking. 



Poor 



Better 



I o o 

! o 





i 







» o 

' o o 



Figure 4-16. — Bearing Blocks in Box Spar. 

4.5. SCARF-JOINTS IN BEAMS. The following requirements should be ob- 
served in specifying scarf joints in solid or laminated beams and beam flanges: 

1. The slope of all scarfs should be not steeper than 1 in 15. The proportion of end 
grain appearing on a scarfed surface is undesirably increased if the material to be spliced 
is somewhat cross-grained, and the scarf is made "across" rather than in the general 
direction of the grain (fig. 4-17). For this reason it is very desirable that the following 
note be added to all beam drawings showing scarf joints: 

Where cross grain loithin the specified acceptable limits is present, all scarf cuts should 
be made in the general direction of the grain slope. 



A 


/A/CORRECT 




8 


INCORRECT 





C CORRECT 

Figure 4-17. — Relationship Between Grain Slope and Scarf Slope. 

2. In laminated members the longitudinal distance between the nearest scarf tips 
in adjacent laminations shall be not less than 10 times the thickness of the thicker 
lamination (fig. 4-18). 

In addition to the previously mentioned specific requirements, it is recommended 
that the number of scarf joints be limited as much as possible; the location be limited 
to the particular portion of a member where margins of safety are most adequate and 
stress concentrations are not serious; and special care be exercised to employ good 
technique in all the preparatory gluing, and pressing operations. 

4.26. Reinforcement of Sloping Grain. Where necessary tapering produces an 
angle between the grain and edge of the piece greater than the allowable slope for the 



216 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



L 



I 



"t" is the thicknesB of the 
thicker lamination. 



1 



Figure 4-18. — Minimum Permissible Longitudinal Separation of Scarf Joints in Adjacent Laminations. 

particular species, the piece should be reinforced to prevent splitting by gluing plywood 
reinforcing plates to the faces (fig. 4-19). 




Figure 4-19.— Solid Wing Spar at Tip. 



4.3. RIBS. 

4.30. Types of Ribs. Rib design has changed very little for several years. See 
N.A.C.A. Technical Report 345 (ref. 2-23). The more common types are the plywood 
web, the lightened plywood web, and the truss. The truss type is undoubtedly the most 
efficient, but lacks the simplicity of the other types. 

For fabric-covered wings the ribs are usually one piece with the cap strips con- 
tinuous across the spars. When plywood covering is used the ribs are usually con- 
structed in separate sections (fig. 4-20). 

Continuous gusset stiffen cap strips in the plane of the rib. This aids in preventing 
buckling and helps obtain better rib-skin glue joints where nail gluing is used because 
such a rib can resist the driving force of nails better than other types. Continuous 
gussets (fig. 4-21) are more easily handled than the many small separate gussets other- 
wise required. 

Any type of rib may be canted to increase the torsional rigidity of a structure such 
as a wood-framework, fabric-covered control surface (fig. 4-22). 

Diagonals loaded in compression are more satisfactory than diagonals loaded in 
tension since tension diagonals are more difficult to hold at the joints. 

4.31. Special Purpose Ribs. Where concentrated loads are introduced, as at 
landing gear or nacelle attachments, bulkhead-type ribs can be used to advantage. 



DETAIL STRUCTURAL DESIGN 



217 



, — RIB CAP5 CONTINUOUS ACR055 5PAR5 




LIGHTENED PLYWOOD WLB TYPE. 
Figure 4-20. — Typical Wing Ribs. 




Figure 4-21. — Rib Employing Continuous Gussets. 




Figure 4-22.— Control Surface Employing Canted Ribs. 



218 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



When this is the case, the rib acts as a chordwise beam, and the principles presented in 
section 4.2 will apply (fig. 4-23). 

B-i 




A— 1 

Figure 4-23. — Special Purpose Ribs. 

4.32. Attachment of Ribs to the Structure. In general, ribs are glued to the adja- 
cent structure by means of corner blocks, plywood angles or gussets, or in special cases, 
by some mechanical means. These are all shown in detail in figures 4-24, 4-25, 4-26, 
4-27, 4-34, and 4-39. 




Figure 4-24. — Typical Rib Attachments to Flush Surface Beams. 



Although the attachment of ribs to I-beams may complicate the rib design, many 
engineers believe that the mechanical shear connection obtained by notching the ribs 
so that the end may be inserted between the I-beam flanges is an advantage since the 
shear connection is not dependent upon quality of the glue joint between the rib and 



DETAIL STRUCTURAL DESIGN 



219 



the beam shear web. This type of connection is shown in figure 4-25. The rib vertical 
also acts as a stiffener for the beam shear web and as a flange spreader. 




LYWOOD PLATE 



THESE CORNER BLOCKS 
ARE OFTEN OMITTED 

CORNER BLOCK 



Figure 4-25. — Typical Rib Attachment to I-Beam. 



CORNER BLOCK EXERT5 
PRESSURE AGAINST BOTH 
THE BEAM AND THE RIB 
VERTICAL MEMBER 




\i_ MEMBER 15 GLUED 
TO THE BEAM BEFORE RIB ATTACHMENT 
TO ACT A5 A LOCATING FIXTURE 



Figure 4-26. — Use of Rib Vertical as Locating Fixture. 



220 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



The end rib verticals of plywood web type ribs are sometimes preassembled to 
plain rectangular spars to act as locating members for rib-to-spar assembly. This is 
shown in figure 4-26. Preassembled locating corner blocks might also be used to ad- 
vantage in other types of rib-to-spar attachments if care is taken to provide sufficient 
backing for plywood webs to which corner blocks are being glued so that sufficient gluing 
pressure can be obtained. 

Canted ribs may be attached to beam members by beveling the ends of the ribs 
or by using corner blocks as shown in figure 4-27. 




Figure 4-27. — Typical Canted Rib to Spar Attachment 

4.4. FRAMES AND BULKHEADS. 

4.40 Types of Frames and Bulkheads. No one type of frame or bulkhead seems 
to be the best for all types of loading, but the laminated ring is probably the best type 
for use as an intermediate stiffening frame. Frames or bulkheads are usually made of 
formed laminated wood, cut or routed from plywood, or are a combination of the two 
(fig. 4-28). 

4.41. Glue Area for Attachment of Plywood Covering. Care must be taken when 
using the routed plywood type of bulkhead that the plywood edge provides sufficient 
gluing area for the skin. It is often necessary to glue solid wood to the face of the ring 
near its edge to provide additional gluing surface. This is illustrated in figure 4-29. 

4.42. Reinforcements for Concentrated Loads. When concentrated loads are car- 
ried into a frame it may be desirable to scarf in some high-density material and brace 
the frame with a plywood web or solid truss members. 

4.5. STIFFENERS. 

4.50. General. The terms "stringer," "stiffener," and "intercostal" are often used 
interchangeably. In the following discussion, "stringer" will refer to members con- 
tinuous through ribs and frames and "intercostal" will refer to members terminating 
at each rib or frame. The term "stiffener" will not be used, since both stringers and 
intercostals act as stiffeners. 



DETAIL STRUCTURAL DESIGN 





Section A-A 

Figure 4-29. — Use of Glue Blocks with Routed Plywood Bulkhead. 



222 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



4.51. Attachment of Stringers. Ribs or frames must be notched if stringers are 

used. A method of reinforcing these notches and fastening the stringers to the rib or 
frame is illustrated in figure 4-30. Attachments may also be made by one of the methods 
shown in figure 4-34. 



A'-i 




- R»inf oreenant - 

Figure 4-30. — Stringer Through Frame Joint. 



4.52. Attachment of Intercostals. All intercostals should be firmly attached to 
ribs or frames. Figure 4-31 illustrates the undesirable practice of terminating inter- 
costals some distance from the rib or frame. This usually results in cleavage along the 
glue line starting at the free end of the intercostal. It is better to butt the stiffeners to 
the rib or frame and fasten them with saddle gussets as illustrated in figure 4-32 or by 
one of the attachments shown in figure 4-34. 




Figure 4-31. — Poor Method of Intercostal Attachment. 




Figure 4-32. — Acceptable Method of Intercostal Attachment. 
4.6. GLUE JOINTS. 

4.60. General. Glue joints should be used for all attachments of wood to wood 
unless concentrated loads, cleavage loads, or other considerations necessitate the use 
of mechanical connections. 

4.61. Eccentricities. Eccentricities and tension components should be avoided in 
glue joints by means of careful design. Figure 4-33 illustrates an example of an eccen- 
tricity and a method of avoiding it. 



DETAIL STRUCTURAL DESIGN 



223 



Skin 



Frame 




1 



. — Frame should be thick enough 
to keep stresses In the glue 
♦P line low. 




Plywood Gusset. An alternate 
method is to carry an inside 
skin to the next frame, form- 
ing a symmetrical box structure. 



Figure 4-33. — Joint in a Shell Structure. 



4.62. Avoidance of End Grain Joints. End grain glue joints will carry no appre- 
ciable load. Strength is given to such a joint by using corner blocks or gussets as shown 
in figure 4-34. These sketches are typical of joints encountered in joining rib members, 
in attaching ribs to beams or intercostals to frames, or any other similar application. 




Square 



Triangular 
Corner Blocks 




Quarter- Round 





lywood gusset should 
lap far enough so that 
the gl ue area is suf- 
ficient to keep the 
stresses low. 



Plywood Angle Plywood Gusset 

Figure 4-34. — Typical Reinforcement of End Grain Joints. 



224 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



4.63. Gluing of Plywood over Wood-Plywood Combinations. Many secondary 
glue joints must be made between plywood covering and wood-plywood structural mem- 
bers having plywood edges appearing on the surface to be glued. Wood-plywood beams 
or wing ribs employing continuous gussets are examples of such members. The plywood 
edge has a tendency to project above the surface thereby preventing contact between 
the plywood covering and the wood portion of the wood-plywood surface. This condition 
can be the result of differential shrinkage between the wood and plywood or may be 
caused by the surfacing machine having a different effect cutting across the grain of the 
plywood from cutting parallel to the grain of the wood. Figure 4-35 shows this condition 
and shows how it can be eliminated by beveling the edges of the plywood. 




Figure 4-35. — Beveling of Plywood Webs and Gussets. 



4.64. Gluing of High-Density Material. Better glue joints can be obtained be- 
tween a high-density material and a relatively soft wood if the surface of the high- 
density material is sanded before gluing. The purpose of sanding is to remove the glazed 
surface present on high-density material and present on some plywoods. Satisfactory 
compreg-to-compreg joints can be made if both surfaces are machined perfectly flat 
immediately prior to gluing. 

4.7. MECHANICAL JOINTS. 

4.70. General. Mechanical Joints in wood are usually limited to types employing 
aircraft bolts. Since bolts in wood can carry a much higher load parallel to the grain 
of the wood than across the grain, it is generally advantageous to design a fitting and its 
mating wood parts so that the loads on the bolts are parallel to the grain. The use of a 
pair of bolts on the same grain line, carrying loads perpendicular to the grain and oppo- 
sitely directed, is likely to increase the tendency to split. When a long row of bolts is 
used to join two parts of a structure, consideration should be given to the relative de- 
formation of the parts, as explained in section 4.82. 

4.71. Use of Bushings. Bushings are often used in wood to provide additional 
bearing area and to prevent crushing of the wood when bolts are tightened (fig. 4-36). 
When bolts of large L/D (length/diameter) ratio are used, or when bolts are used through 
a member having high-density plates on the faces, plug bushings may be used to advantage. 

4.72. Use of High-Density Material. Wherever highly concentrated loads are in- 
troduced, greater bearing strength can be obtained by scarfing-in high-density material 
(sec. 4.63). Some high density materials are quite sensitive to stress concentrations and 
the possibility of the serious effects of such stress concentrations should be considered 
when large loads must be carried through the high-density material. 



DETAIL STRUCTURAL DESIGN 



225 




Through bushing made 
slightly shorter than 
the width of the beam. 




Throurh Bushing 



Plug Bushing 



Figure 4-36. — Types of Bushings. 



Wherever metal fittings are attached to wood members, it is generally advisable to 
reinforce the wood against crushing by the use of high-density bearing plates (fig. 4-37), 
and to use a coat of bitumastic or similar material between the wood and metal to guard 
against corrosion. Cross banding of these plates will help to prevent splitting of the solid 
wood member. 



1 1 : ' 1 



if 



i i — r 
i — r 



l — r 



■OfiBBS 




High Density 
Material 



Metal Fitting 




Cross Banded Filler Block 

Figure 4-37. — Typical Wing Beam Attachment. 



226 



ANC BULLETIN 



— DESIGN OF 



WOOD AIRCRAFT STRUCTURES 




HIGH DENSITY 
BEARING PLATE 



Fioure 4-38. — Distribution of Crushing Loads. 



4.7 3. Mechanical Attachment of Ribs. When ribs carry heavy or concentrated 
loads it is sometimes desirable to insure their attachment by use of mechanical fastenings 
(fig. 4-39). 




TO 



TO THE! SPAR BY MEAN5 OF TO THE. SPAR BY MEAN5 OF 

METAL ANGLES. METAL CLIPS 

Figure 4-39. — Mechanical Attachment of Ribs. 



4.74. Attachment of Various Types of Fittings. Fittings should have wide base 
plates to prevent crushing at edges. Wood washers have a tendency to cone under tight- 
ening loads. Where possible, it is desirable to use washer plates for bolt groups, as illus- 
trated in figure 4-40, but if washers are used, a special type for wood, AN-970 or equiva- 
lent, are necessary to provide sufficient bearing area. 

Clamps around wood members should be constructed so that they can be tightened 
symmetrically (fig. 4-41). , 

4.7 5. Use of Wood Screws, Rivets, Nails, and Self-Locking Nuts. Wood screws 
and rivets are sometimes used for the attachment of secondary structure but should not 
be used in connecting primary members. Wood screws have been successfully used to 
prevent cleavage of plywood skin from stringers in some skin-stringer applications. 
Nails should never be used in aircraft to carry structural loads. 

Self-locking nuts of approved types designed for use with wood and plywood 
structures are preferable to plate or anchor nuts. When the latter type is used, however, 
attachment may be made to the structure with wood screws or rivets provided that 
care is taken not to reduce the strength of load-carrying members. Riveting through 
wood is always questionable because of the danger of crushing the wood under the rivet 
heads and the possibility of bending the shank while bucking the rivet. Also, there is 



DETAIL STRUCTURAL DESIGN 



227 




Figure 4-41. — Installation of Clamp Fittings. 

no way of tightening the joint when dimensional changes from shrinkage occur. 
4.8. MISCELLANEOUS DESIGN DETAILS. 

4.80. Metal to Wood Connections. Metal to wood connections are complicated 
by an inherent weakness of all untreated wood— low shear and bearing strength. Sec- 
tions 4.6 and 4.7 present various methods of minimizing this drawback. 

Another way of improving the efficiency of wood structures is to keep the number 
of joints to a minimum. For example, when other design considerations will permit, a 
one-piece wood wing is desirable; when this is not permissible, the wing joint should be 
placed as far outboard as possible so that the fitting loads will be low. 

4.81. Stress Concentrations. Since wood in tension has practically no elongation 
between the proportional limit and the ultimate strength, there is little of the "internal 
adjustment" common to metal structures. Stress concentrations, therefore, become 
more critical and, for efficient design, must be held to a minimum. The fact that com- 
preg and similar materials are very sensitive to stress concentrations should be carefully 
considered when these materials are used. 



228 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 



4.82. Behavior of Dissimilar Materials Working Together. When materials of 
differing rigidities, such as normal wood, compreg, or metal fittings, are fastened to- 
gether for a considerable distance and are under high stress, consideration should be 
given to the fact that the fastening causes the total deformation of all materials to be the 
same. A typical example is a long metal strap bolted to a wood spar flange for the pur- 
pose of taking the load out of the wood at a wing joint. In order that the load be uni- 
formly distributed among the bolts, the ratio of the stress to the modulus of elasticity 
should be the same for both materials at every point. This may be approximated in 
practical structures by tapering the straps and the wood in such a manner that the 
average stress in each (over the length of the fastening) divided by its modulus of 
elasticity gives the same ratio. 

When splicing high-density materials to wood, or in dropping off bearing plates, 
the slope of the scarf should be less steep than the slope allowed for normal wood. 

4.83. Effects of Shrinkage. When the moisture content of a piece of wood is 
lowered its dimensions decrease. The dimensional change is greatest in a tangential 
direction (across the fibers and parallel to the growth rings), somewhat less in a radial 
direction (across the fibers and perpendicular to the growth rings), and is negligible in a 
longitudinal direction (parallel to the fibers). For this reason a flat-grained board will 
have a greater change in width for a given moisture content change than an edge- 
grained board. Flat-grained boards also have a greater tendency to warp than do edge- 
grained boards. 

These dimensional changes can have several deleterious effects upon a wood structure 
and the designer must study each case to determine which effects are most harmful, 
and which are the most satisfactory methods of minimizing them. Loosening of fittings 
and wire bracing are common results of shrinkage. Checking or splitting of wood 
members frequently occurs when shrinkage takes place in members that are restrained 
against dimensional change. Restraint is sometimes given by metal fittings and quite 
often by plywood reinforcements since plywood shrinkage is roughly only 1/20 of cross 
grain shrinkage of solid wood. 

A few of the methods of minimizing these shrinkage effects are: 

1. Use bushings that are slightly short so that when the wood member shrinks 
the bushings do not protrude and the fittings may be tightened firmly against the 
member (fig. 4-36). 

2. Place the wood so that the more important face, in regard to maintaining dimen- 
sion, is edge-grained. For example, solid spars are required to be edge-grained on their 
vertical face so that the change in depth is a minimum. 




Figure 4-42. — Protection Against Splitting. 



I 

DETAIL STRUCTURAL DESIGN 229 



3. Wood members can be reinforced against checking or splitting by means of 
plywood inserts or cross bolts (fig. 4-42). Care should be taken to avoid constructions 
that introduce cleavage (cross-grain) loads when shrinkage occurs. 

4. Plywood face plates should be dropped off gradually either by feathering or 
by shaping so that the cleavage loads at the edge of the plywood are minimized when 
shrinkage occurs (fig. 4-43). 

fEATHERED END7 SPADED END 7 




4.84. Drainage and Ventilation. Wood structures must be adequately drained 
to insure a normal length of service life. This applies to box spar sections as well as all 
low portions of wings and fuselages. The usual method is to drain each compartment 
separately as illustrated in figure 4-44. Another acceptable method is to drain from 
one compartment to another until the lowest compartment is reached, or structural 
requirements prohibit further internal drainage, before drainage holes to the exterior 
are bored. This method is illustrated in figure 4-45. 




:l/4 inch holes drilled at the 
low points of all compartments 



Figure 4-44. — Drainage Diagram of Wing, Direct Method. 



Service experience indicates that drainage holes for individual compartments 
should be not less than one-quarter inch in diameter, with three-eighths inch being 
preferable. Drainage holes to the exterior used with the internal drainage system should 
probably be somewhat larger. If the internal drainage system is used it is suggested 



230 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




A- A 1/2 inch holes drilled at the low 

point of the lowest compartments - 



Figure 4-45. — Drainage Diagram of Wing, Internal Method. 

that the inter-compartment drainage holes be inspected after the internal finish has 
been applied to make sure that the finish has not clogged the internal drain holes. This 
will necessitate attaching the top skin last. 

Drain holes are usually drilled from the external surface so that the splintering 
does not mar the external finish. After drilling drain holes, all splinters should be care- 
fully removed from the inner surface, and the edges of the holes should be sanded 
lightly and protected by the application of several coats of spar varnish. It is common 
practice, in order to avoid damage to structural members by the drill, to drill drainage 
holes an appreciable distance from the low corner of a compartment. This practice 
must be avoided and some method of insuring proper location of drain holes at the 
actual low points must be developed by the aircraft manufacturer that will not only 
prevent damage to the framework but will also provide complete drainage of the 
structure. 

It is, therefore, recommended that proof of the adequacy of the drainage system 
chosen be demonstrated by setting up the structure, with the top cover removed, in a 
position corresponding to its attitude when the airplane is resting on the ground. Water 
is then poured into the structure and the actual performance of the drainage system 
observed. 

Careful design to prevent entry of water into the structure is equally important. 
Careful location of all openings and use of boots and gaskets should be considered. If 
interiors do happen to get wet, good ventilation will accelerate the drying. Marine 
grommets have been suggested for use with external drain holes in wing, tail, and control 
surfaces. This type of grommet produces a suction or scavenging action in flight and 
also protects the holes themselves from direct splash during taxiing on wet or muddy 
fields. Periodic inspection and cleaning of drainage holes covered with marine grommets, 
however, may be difficult. 

4.8 5. Internal Finishing. It is recognized that applying finish to the inner surfaces 



DETAIL STRUCTURAL DESIGN 



231 



of the closing panels of plywood-covered structures is a difficult problem. The usual 
method, other than dipping, is to mask off the locations of secondary glue areas prior 
to the application of finish to the surface, for wood coated with a protective finish can- 
not be glued. This is a time-consuming operation, and after the plywood covering is 
finally fitted into place, the film of finish usually stops short of the intersection lines 
between the plywood covering and framework. These are the very places where the 
finish is needed most if water does accumulate in the interior. 

Wood-rotting organisms can act only if the moisture content of the wood is above 
approximately 20 to 25 percent. Although finishes will not prevent moisture content 
changes in wood, they will retard such changes so that the wood moisture content will 
not follow the rapid changes in atmospheric conditions but only the more gradual 
changes. Therefore, if wood members are finished, dangerously high moisture contents 
will be reached in wood aircraft structures only when parts are in contact with standing 
water since atmospheric conditions that produce high moisture contents are generally 
of relatively short duration, except in extreme climates such as the tropics, and the 
retarding effect of the finish may be expected to prevent the wood from attaining a 
high moisture content within this short period. 

In view of the foregoing discussion, it is suggested that consideration be given to 
the following method of finishing the inner surfaces of plywood-covered assemblies. 
Since any free water would be in contact with the lower skin almost entirely, the lower 
wing covering and control surface coverings should be attached to the framework prior 
to the upper covering. In this way, finish can be applied thoroughly to the lower cover- 
ing and adjacent framework quite easily after the assembly gluing operation has been 
completed. Since gaps in the finish on the upper covering along framework members 
are not so harmful as they would be on the inner surfaces of the lower covering, wider 
masking strips may be used over secondary glue areas on the upper covering at the time 
of applying the internal finish, thereby reducing the chance of finished surfaces falling- 
over framework members. Some method of accurately registering the covering should 
be used. 

4.86. External Finishing. Two types of external finish for plywood covered air- 
craft have been used successfully, the direct-to-plywood finish and the fabric-covered 
plywood finish. There is little difference in weight between the two systems because 
the weight of the fabric is offset by the difference in weight between the finishes used 
in the two systems. 

Direct-to-plywood finishes have a tendency to check wherever a glue joint appears 
on the surface. Checking of the finish is also apt to occur when the grain of the wood 
tends to raise, as in those softwoods having appreciable contrast between spring and 
summerwood, such as Douglas-fir. Fabric-covered finishes do not check from these 
causes. 

Light airplane fabric of the type specified in AN-C-83 is the usual material used 
for the fabric-covered plywood finish system. The fabric provides a better protection 
from the abrasive action of stones, sand, and other objects kicked up while taxiing 
than does the direct-to-plywood finish. 

Observation of wood airplanes in service has revealed that plywood or fiber plates 
glued over exposed end grain may act as a moisture trap rather than as a moisture 
barrier. Several coats of brushed-in aluminized spar varnish are believed to give a much 



232 



ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



more satisfactory protection to exposed end grain. Exposed end grain should be 
interpreted to include exposed feathered surfaces. 

4.87. Selection of Species. Properties other than the usually listed strength and 
elastic properties should also be considered when selecting a wood for any specific 
purpose. For example, birch and maple are relatively difficult to glue; yellowpoplar 
has lower resistance to shock than spruce; Douglas-fir is low in cleavage strength. 

4.88. Use of Standard Plywood. From a maintenance viewpoint it is desirable 




FUSELAGE PANEL 




FUSELAGE NOSE SECTION 

Figure 4-46. — Fuselage Framework. 



DETAIL STRUCTURAL DESIGN 233 

to use only standard plywoods for design so that too great a variety of types will not 
need to be carried in stock. Table 2 9 lists many of the more common constructions. 
If one of these is used, the formulas in chapter 2 can be used with greater ease because 
many of the basic parameters and strength values are given in this table. Two-ply 
diagonal plywood is considered a special construction by most plywood manufacturers 
and has the disadvantage of tending to warp because of its unsymmetrical construction. 

4.89. Tests. Quite often, time and effort may be saved by the use of simple tests 
in the early stages of the design of complex joints. 

4.9. EXAMPLES OF ACTUAL DESIGN DETAILS. 

On the following pages several sketches and photographs are presented to show 
how various manufacturers have treated details encountered in the design of wood 
aircraft. No effort has been made to label these sketches as either good or poor practice. 
They are merely presented to show what the industry has done when confronted with 
specific problems (figs. 4-46 through 4-63). 



234 



ANC BULLETIN— DESTGN OF WOOD AIRCRAFT STRUCTURES 



?0UTED SPRUCE 



- MAHOGANY- POPLAR 
PLYWOOD 



-DRAINAGE AND VENTILATION 1 
HOLES 



FIN BEAM 



WALNUT- POPLAR — 
PLYWOOD PLATE5 




AIRPLANE 




WING BEAM 

SHOWING BLOCKING AND PLATING AT LOCATION 
OF APPLICATION OF CONCENTRATED LOAD5 



Figure 4-47. — Examples of Beams. 



DETAIL STRUCTURAL DESIGN 



235 





End Doaljrn. 

Th« following changes from the 
orlglaaJ. design were Incorpora- 
ted. 

1. Bearing bloolta Item 1 removed. 

2. Faoo plat© item 6 added. 

S. find aeotlon of item 3 outout 
and apruoe wedges Item 6 in- 
stalled with.jgreln porpindi- 
oular to thfj spir axi o . 
Failure ooourrai to indicated « 
B, - 10,100 f 
U. - 7600 # 
BJ1 - 183,063 in. lb*. 




3rd Design. 

The following ohengea from the 
2nd design were incorporated . 
1* Tertioel grain ipruoe wedges 
Item 6 eliminated. 

2. Hotel straps added* 

3. Bolt and bearing plates added* 
Loaded tot 

B, «= 21,400 
Hp «' 16,100 
B.H - 367,676 in. lbs* 
without failure. 



HITERIAL BOTES 



@ J" Mapl* 

(7^ 1/8"- 3 Ply Mahogany 

(Tlj 1" Spruoe 

(T^ i"- 46°- 4 Ply Mahogany 

fs«) 4 Ply Mahogany 

^— ^ (Faoe Grain Parallel to Spar Axis) 

(7l) Sprue* * (Grain Perpandloula* to Spar Axis) 



Figure 4-48.— Cantilever Wood Spar at Fuselage Attachment. 



DETAIL STRUCTURAL DESIGN 



237 




Figure 4-50.— Spar Details at Root Section and Fuselage Attachment. 



238 



ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




Figure 4-51. — Further Spar Details at Root Section and Fuselage Attachment. 



DETAIL STRUCTURAL DESIGN 



230 





Figure 4-54. — Method of Double Drag Bracing. 



DETAIL STRUCTURAL DESIGN 



241 




Figure 4-55. — Attachment of Flap Hinge. 



242 



ANC BULLETIN — DESIGN OP WOOD AIRCRAFT STRUCTURES 




Figure 4-56. — Attachment of Empennage. 



DETAIL STRUCTURAL DESIGN 



243 




<m **** 1 



9 PLY 

mah - po plar 

1 Ply w o 



S,TCA/0/V F ~ F 



Figure 4-57. — Reinforced Fuselage Frame. 



244 ANC BULLETIN — DESIGN OF WOOD AIRCRAFT STRUCTURES 



DETAIL STRUCTURAL DESIGN 



245 




r— METAL TORQUE. TUBE 




Figure 4-60. — Example of Elevator Torque Tube Attachment to Control Surface. 



246 ANC BULLETIN— DESIGN OF WOOD AIRCRAFT STRUCTURES 




MUST BE. FLUSH (FIRLWALL INSTALLATION) 

Figure 4-62. — Typical Fuselage Joint or Engine Mount Attachment. 



I 



I 



MEMORANDUM 



1 

MEMORANDUM 



■ 



MEMORANDUM 



MEMORANDUM